text:
\section{Introduction}

Among a large number of studies conducted on the
relationship between thermodynamics and information
processing, particularly provoking is the work of
Szilard who argued that positive work $W_{ext}$ can be
extracted from an isothermal cycle if Maxwell's demon
plays the role of a feedback controller.\, It is now well understood that the role of the demon does not contradict the second law of thermodynamics, because the initialization of the demon's memory entails heat dissipation.\, We note that, in the case of an isothermal process, the second law of thermodynamics can be expressed as

\begin{equation}
W_{ext}\leq-\Delta{F^S}
\end{equation}
where $\Delta{F^S}$ is the difference in the Helmholtz free energy between the initial and final thermodynamic equilibrium states.

In a different context, quantum feedback control has attracted considerable attention for controlling and stabilizing a quantum system.\, It can be applied, for example, to squeezing an electromagnetic field, spin squeezing, and stabilizing macroscopic coherence.\, While the theoretical framework of quantum feedback control as a stochastic dynamic system is well developed, the possible thermodynamic gain of quantum
feedback control has yet to be fully understood.\\

In this Letter, we derive a new thermodynamic inequality which sets the fundamental limit on the work that can be extracted from multi-heat-baths with discrete quantum feedback control, consisting of quantum measurement and a mechanical operation depending on the measurement outcome.\, The maximum work is characterized by a generalized mutual information content between the thermodynamic system and the feedback controller.
We consider a thermodynamic process for system S
which can contact heat baths $B_{1}$; $B_{2}$; . . . ; $B_{n}$ at respective temperatures $T_{1}$; $T_{2}$; . . . ; $T_{n}$.\, We assume that system S is in
thermodynamic equilibrium in the initial and final states. For simplicity, we also assume that the initial and final temperature of S is given by $T={{\left( {{k}_{B}}\beta  \right)}^{-1}}$. This can be
realized by contacting S with, for example, B1 in the
preparation of the initial state and during equilibration to the final state; in this case $T={{T}_{1}}$.\, We do not, however, assume that the system is in thermodynamic equilibrium between the initial and final states. Then the second law of thermodynamics is expressed as the Clausius inequlity:
\begin{equation}
\sum\limits_{m}{{{\beta }_{m}}{{Q}_{m}}\le 0}
\end{equation}

\section{Nonextensive Concepts}

Methods of nonextensive statistical mechanics have found use in
much many topics of physics and other sciences.\, In the nonextensive statistical physics, the Tsallis q-entropy of the probability distribution p is defined as

\begin{equation}
{{H}_{q}}(p)=\frac{1}{q-1}\left( \sum\limits_{i=1}^{m}{p_{i}^{q}-1} \right)=-\sum\limits_{i=1}^{m}{p_{i}^{q}{{\ln }_{q}}{{p}_{i}}}
\end{equation}
where ${{\ln }_{q}}x=\frac{{{x}^{1-q}}-1}{1-q}$ is q-logarithm function.The quantum Tsallis entropy of density operator $\rho$ is defined as:
\begin{equation}
{{S}_{q}}(\hat\rho )=\frac{1}{1-q}tr\left( {{\hat\rho }^{q}}-\hat\rho  \right)
\end{equation}
For $q = 1$, we have the von Neumann entropy $S(\hat\rho )=-tr(\hat\rho \ln \hat\rho )$.

\section{Q-functions in Canonical Ensemble}

Canonical equilibrium distribution in nonextensive statistical is defined as:
\begin{equation}
{{\hat\rho }_{q}}=\frac{e_{q}^{-{\beta }'\hat{H}}}{{{{\bar{Z}}}_{q}}}
\end{equation}
where in equation (5)
\begin{equation}
{{\bar{Z}}_{q}}=tr\left( e_{q}^{-{\beta }'\hat{H}} \right)
\end{equation}
and
\begin{equation}
{\beta }'=\frac{\beta }{\sum\nolimits_{i=1}^{w}{{{\left( {{p}_{i}} \right)}^{q}}+\left( 1-q \right)\beta {{U}_{q}}}}
\end{equation}
With the canonical distribution, free energy $F^S$ can be calculated as
\begin{equation}
{{F}_{q}}=-{{k}_{B}}T{{\ln }_{q}}{{Z}_{q}}
\end{equation}
where
\begin{equation}
{{\ln }_{q}}{{Z}_{q}}={{\ln }_{q}}{{\bar{Z}}_{q}}-\beta {{U}_{q}}
\end{equation}
The average of measurement outcomes of observable A is given by
\begin{equation}
{{\left\langle A \right\rangle }_{q}}=tr\left( {{\hat\rho }^{q}}A \right)
\end{equation}

\section{Q-Clausius inequality}
We consider a thermodynamic process of system S that can contact heat baths  $B_{1}$; $B_{2}$; . . . ; $B_{n}$ and we assume that the total of S and $B_{m}$'s obeys a unitary evolution.\, The total Hamiltonian can be written as
\begin{equation}
\hat{H}(\lambda ,\left\{ {{c}_{m}} \right\})={{\hat{H}}^{S}}(\lambda )+\sum\limits_{m=1}^{n}{({{{\hat{H}}}^{S{{B}_{m}}}}({{c}_{m}})+{{{\hat{H}}}^{{{B}_{m}}}})}
\end{equation}
where ${\hat{H}}^{S}(\lambda )$ is the Hamiltonian of S, ${{{\hat{H}}}}^{S{{B}_{m}}}({{c}_{m}})$ is the interaction Hamiltonian between S and ${B}_{m}$, and ${{{\hat{H}}^{{B}_{m}}}}$ is the Hamiltonian of ${B}_{m}$. Here, $\lambda$ describes controllable
external parameters, and ${c}_{m}$ describes external parameters to control the interaction
between S and ${B}_{m}$.

We assume that the initial state of the total system is given by
\begin{equation}
{{\hat\rho }_{i}}=\hat\rho _{i}^{s}\otimes \hat\rho _{q}^{{{B}_{1}}}\otimes ...\otimes \hat\rho _{q}^{{{B}_{n}}}
\\
\end{equation}
The process with unitary evolution of the total system, $\hat{U}\equiv T\exp \left( -i\int\limits_{0}^{\tau }{\hat{H}(\lambda (t),\left\{ {{c}_{m}}(t) \right\})dt} \right)$ leads to the final state
\begin{equation}
{{\hat\rho }_{f}}\equiv \hat{U}{{\hat\rho }_{i}}{\hat{U}^{\dagger }}
\end{equation}
Then the Tsallis entropy of initial state of total system is given by
\begin{equation}
\begin{aligned}
& {{S}_{q}}({{\hat\rho }_{i}})=-tr\left( \hat\rho _{i}^{q}{{\ln }_{q}}{{\hat\rho }_{i}} \right)={{S}_{q}}(\hat\rho _{i}^{s})tr(\hat\rho _{q}^{q{{B}_{1}}})...tr(\hat\rho _{q}^{q{{B}_{n}}})+ \\
& \sum\limits_{m}{\frac{{{{{\beta }'}}_{m}}}{{{{\bar{Z}}}_{m}}^{1-q}}\left( tr\left[ \hat\rho _{q}^{q{{B}_{m}}}{\hat{H}^{{{B}_{m}}}} \right]+\frac{1}{{{{{\beta }'}}_{m}}}tr\left( \hat\rho _{q}^{q{{B}_{m}}}{{\ln }_{q}}{{Z}_{mq}} \right)+\frac{{{\beta }_{m}}}{{{{{\beta }'}}_{m}}}tr\left( \hat\rho _{q}^{q{{B}_{m}}}{{U}_{mq}} \right) \right)} \\
& tr(\hat\rho _{i}^{sq})-(1-q)\left[ tr\left( \hat\rho _{i}^{sq}{{\ln }_{q}}{{\hat\rho }_{i}}\otimes \hat\rho _{q}^{q{{B}_{1}}}{{\ln }_{q}}\hat\rho _{q}^{{{B}_{1}}}\otimes ...\otimes \hat\rho _{q}^{q{{B}_{m}}}{{\ln }_{q}}\hat\rho _{q}^{{{B}_{m}}} \right) \right] \\
\end{aligned}
\end{equation}
From Klein's inequality, we also have
\begin{equation}
\begin{aligned}
& {{S}_{q}}({{\hat\rho }_{f}})\le -tr\left( \hat\rho _{f}^{q}{{\ln }_{q}}(\hat\rho _{f}^{s}\otimes \hat\rho _{q}^{{{B}_{1}}}\otimes ...\otimes \hat\rho _{q}^{{{B}_{n}}} \right)= \\
& -tr\left( \hat\rho _{f}^{q}{{\ln }_{q}}{{\hat\rho }_{f}} \right)={{S}_{q}}(\hat\rho _{f}^{s})tr(\hat\rho _{q}^{q{{B}_{1}}})...tr(\hat\rho _{q}^{q{{B}_{n}}})+ \\
& \sum\limits_{m}{\frac{{{{{\beta }'}}_{m}}}{{{{\bar{Z}}}_{m}}^{1-q}}\left( tr\left[ \hat\rho _{q}^{q{{B}_{m}}}{\hat{H}^{{{B}_{m}}}} \right]+\frac{1}{{{\beta }'}}tr\left( \hat\rho _{q}^{q{{B}_{m}}}{{\ln }_{q}}{{Z}_{mq}} \right)+\frac{{{\beta }_{m}}}{{{{{\beta }'}}_{m}}}tr\left( \hat\rho _{q}^{q{{B}_{m}}}{{U}_{mq}} \right) \right)} \\
& tr(\hat\rho _{f}^{sq})-(1-q)\left[ tr\left( \hat\rho _{i}^{sq}{{\ln }_{q}}{{\rho }_{i}}\otimes \hat\rho _{q}^{q{{B}_{1}}}{{\ln }_{q}}\hat\rho _{q}^{{{B}_{1}}}\otimes ...\otimes \hat\rho _{q}^{q{{B}_{m}}}{{\ln }_{q}}\hat\rho _{q}^{{{B}_{m}}} \right) \right] \\
\end{aligned}
\end{equation}
Therefore we obtain
\begin{equation}
\begin{aligned}
& \left( {{S}_{q}}(\hat\rho _{f}^{s})-{{S}_{q}}(\hat\rho _{i}^{s}) \right)tr(\hat\rho _{q}^{q{{B}_{1}}})...tr(\hat\rho _{q}^{q{{B}_{n}}})\ge  \\
& \sum\limits_{m}{\frac{{{{{\beta }'}}_{m}}}{{{{\bar{Z}}}_{m}}^{1-q}}\left[ tr\left[ \hat\rho _{i}^{q}{\hat{H}^{{{B}_{m}}}} \right]-tr\left[ \hat\rho _{f}^{q}{\hat{H}^{{{B}_{m}}}} \right] \right]}+ \\
& \sum\limits_{m}{\frac{1}{{{{{\beta }'}}_{m}}}\left[ tr\left( \hat\rho _{i}^{q}{{\ln }_{q}}{{Z}_{mq}} \right)-tr\left( \hat\rho _{f}^{q}{{\ln }_{q}}{{Z}_{mq}} \right) \right]}+ \\
& \sum\limits_{m}{\frac{{{\beta }_{m}}}{{{{{\beta }'}}_{m}}}\left[ tr\left( \hat\rho _{i}^{q}{{U}_{mq}} \right)-tr\left( \hat\rho _{f}^{q}{{U}_{mq}} \right) \right]}+ \\
& (1-q)\left[ {{S}_{q}}({{\hat\rho }_{{{B}_{1}}}})...{{S}_{q}}({{\hat\rho }_{{{B}_{m}}}}) \right]\left[ {{S}_{q}}(\hat\rho _{f}^{s})-{{S}_{q}}(\hat\rho _{i}^{s}) \right] \\
\end{aligned}
\end{equation}
and in summary
\begin{equation}
\begin{aligned}
& \left( {{S}_{q}}(\hat\rho _{f}^{s})-{{S}_{q}}(\hat\rho _{i}^{s}) \right)tr(\hat\rho _{q}^{q{{B}_{1}}})...tr(\rho _{q}^{q{{B}_{n}}})\ge  \\
& \sum\limits_{m}{\frac{{{{{\beta }'}}_{m}}}{{{{\bar{Z}}}_{m}}^{1-q}}{{Q}_{qm}}}+\sum\limits_{m}{\frac{{{\beta }_{m}}}{{{{{\beta }'}}_{m}}}\left[ tr(\hat\rho _{i}^{q})-tr(\hat\rho _{f}^{q}) \right]\left( F_{mq}^{B}-U_{mq}^{B} \right)} \\
& +(1-q)\left[ {{S}_{q}}({{\hat\rho }_{{{B}_{1}}}})...{{S}_{q}}({{\hat\rho }_{{{B}_{m}}}}) \right]\left( {{S}_{q}}(\hat\rho _{f}^{s})-{{S}_{q}}(\hat\rho _{i}^{s}) \right) \\
\end{aligned}
\end{equation}
where
\begin{equation}
{{Q}_{qm}}=\left[ tr\left( \hat\rho _{i}^{q}{\hat{H}^{mB}} \right)-tr\left( \rho _{f}^{q}{\hat{H}^{mB}} \right) \right].
\end{equation}
is the heat that is absorbed by system S from heat bath ${B}_{m}$ and ${{U}_{mq}}=-\frac{\partial }{\partial \beta }{{\ln }_{q}}{{Z}_{mq}}$ is internal energy of baths and third term in equation (17) determind interaction between system and baths.
Note for $q=1$ Inequality q-Clausius becomes standard inequality Clausius.

Isothermal process. We next consider the case in which there is a single heat bath.\, We then assume that the initial state of S is the canonical distribution as
\begin{equation}
\hat\rho _{iq}^{s}=\frac{e_{q}^{-{\beta }'\hat{H}_{i}^{s}}}{{{{\bar{Z}}}_{q}}}
\end{equation}
where $\bar{Z}_{iq}^{s}=tr\left( e_{q}^{-{\beta }'\hat{H}_{i}^{s}} \right)$.We also introduce notations as
\begin{equation}
F_{iq}^{s}=-{{k}_{B}}T{{\ln }_{q}}Z_{iq}^{s}
\end{equation}
\begin{equation}
\hat\rho _{fq}^{s}=\frac{e_{q}^{-{\beta }'\hat{H}_{f}^{s}}}{{{{\bar{Z}}}_{q}}}, \bar{Z}_{fq}^{s}=tr\left( e_{q}^{-{\beta }'\hat{H}_{f}^{s}} \right),  F_{fq}^{s}=-{{k}_{B}}T{{\ln }_{q}}Z_{fq}^{s}
\end{equation}
Then the Tsallis entropy of initial and final state of  system is given by
\begin{equation}
\begin{aligned}
& {{S}_{q}}\left( \hat\rho _{iq}^{s} \right)=-tr\left( \hat\rho _{iq}^{sq}{{\ln }_{q}}{{\hat\rho }_{iq}} \right)= \\
& \frac{{{\beta }'}}{\bar{Z}_{iq}^{1-q}}\left[ tr\left( \hat\rho _{iq}^{sq}\hat{H}_{i}^{s} \right)+\frac{1}{{{\beta }'}}tr\left( \rho _{iq}^{sq}{{\ln }_{q}}Z_{iq}^{s} \right)+\frac{\beta }{{{\beta }'}}tr\left( \hat\rho _{iq}^{sq}U_{iq}^{s} \right) \right] \\
\end{aligned}
\end{equation}
and
\begin{equation}
{{S}_{q}}\left( \hat\rho _{fq}^{s} \right)=\frac{{{\beta }'}}{\bar{Z}_{fq}^{1-q}}\left[ tr\left( \hat\rho _{fq}^{sq}\hat{H}_{f}^{s} \right)+\frac{1}{{{\beta }'}}tr\left( \hat\rho _{fq}^{sq}{{\ln }_{q}}Z_{fq}^{s} \right)+\frac{\beta }{{{\beta }'}}tr\left( \hat\rho _{fq}^{sq}U_{fq}^{s} \right) \right]
\end{equation}
From Klein's inequality, we obtain
\begin{equation}
\begin{aligned}
& {{S}_{q}}\left( \hat\rho _{fq}^{s} \right)-{{S}_{q}}\left( \hat\rho _{iq}^{s} \right)\le \frac{{{\beta }'}}{\bar{Z}_{fq}^{1-q}}E_{f}^{s}-\frac{{{\beta }'}}{\bar{Z}_{iq}^{1-q}}E_{i}^{s}-\frac{\beta }{\bar{Z}_{fq}^{1-q}}F_{fq}^{s}tr\left( \hat\rho _{fq}^{sq} \right)+ \\
& \frac{\beta }{\bar{Z}_{iq}^{1-q}}F_{iq}^{s}tr\left( \hat\rho _{iq}^{sq} \right)+\frac{\beta }{\bar{Z}_{fq}^{1-q}}U_{fq}^{s}tr\left( \hat\rho _{fq}^{sq} \right)-\frac{\beta }{\bar{Z}_{iq}^{1-q}}U_{iq}^{s}tr\left( \hat\rho _{iq}^{sq} \right) \\
\end{aligned}
\end{equation}
where
\begin{equation}
E_{i}^{s}=tr\left( \hat\rho _{iq}^{sq}\hat{H}_{i}^{s} \right)
\end{equation}
and
\begin{equation}
E_{f}^{s}=tr\left( \hat\rho _{fq}^{sq}\hat{H}_{f}^{s} \right)
\end{equation}
are energy stored in the system.\,that is clear for $q=1$ equation (24) becomes the standard form as follow
\begin{equation}
S\left( \hat\rho _{f}^{s} \right)-S\left( \hat\rho _{i}^{s} \right)\le \beta \left( \Delta {{E}^{s}}-\Delta {{F}^{s}} \right)
\end{equation}

\section{Entropy-Mutual Information Inequality}
We derive the entropy balance of a quantum system that obeys a quantum measurement and quantum feedback control in addition to unitary evolutions.
Let ${{\hat{\rho }}_{i}}$ be an arbitrary initial density operator of quantum system,\,which evolves as follows.\\

Step 1: Unitary evolution. From time 0 to $t_1$, the system undergoes unitary evolution ${{\hat{U}}_{i}}$. At time t1, the density operator is given by ${{\hat{\rho }}_{1}}={{\hat{U}}_{i}}{{\hat{\rho }}_{i}}\hat{U}_{i}^{\dagger }$.

Step 2: Measurement. From time $t_1$ to $t_2$, we perform a quantum measurement on the system. We assume that the measurement is described by measurement operators
$\left\{ {{{\hat{M}}}_{k}} \right\}$ with k's being measurement outcomes, which leads to POVM
\begin{equation}
{{\hat{E}}_{k}}\equiv \hat{M}_{k}^{\dagger }{{\hat{M}}_{k}}
\end{equation}
The post-measurement state corresponding to outcome k is given by
\begin{equation}
\hat{\rho }_{2}^{(k)}\equiv \frac{1}{{{p}_{k}}}{{\hat{M}}_{k}}{{\hat{\rho }}_{1}}\hat{M}_{k}^{\dagger }
\end{equation}
and the ensemble average is given by
\begin{equation}
{{\hat{\rho }}_{2}}=\sum\limits_{k}{{{p}_{k}}\hat{\rho }_{2}^{\left( k \right)}}=\sum\limits_{k}{{{{\hat{M}}}_{k}}{{{\hat{\rho }}}_{1}}\hat{M}_{k}^{\dagger }}
\end{equation}

Step 3: Feedback control. From  $t_2$ to  $t_3$, we perform feedback control; the corresponding unitary operator ${{\hat{U}}_{k}}$ depends on measurement outcome k. The postfeedback state corresponding to outcome k is given by
\begin{equation}
\hat{\rho }_{3}^{(k)}={{\hat{U}}_{k}}\hat{\rho }_{2}^{(k)}\hat{U}_{k}^{\dagger }=\frac{1}{{{p}_{k}}}{{\hat{U}}_{k}}{{\hat{M}}_{k}}{{\hat{\rho }}_{1}}\hat{M}_{k}^{\dagger }\hat{U}_{k}^{\dagger }
\end{equation}
and the ensemble average is given by
\begin{equation}
{{\hat{\rho }}_{3}}=\sum\limits_{k}{{{p}_{k}}{{{\hat{U}}}_{k}}\hat{\rho }_{2}^{(k)}\hat{U}_{k}^{\dagger }}=\sum\limits_{k}{{{{\hat{U}}}_{k}}{{{\hat{M}}}_{k}}{{{\hat{\rho }}}_{1}}\hat{M}_{k}^{\dagger }\hat{U}_{k}^{\dagger }}
\end{equation}

Step 4: Unitary evolution. After the feedback, from time $t_3$ to $\tau $, the system evolves
according to unitary operator ${{\hat{U}}_{f}}$ which is independent of outcome k. The final state is ${{\hat{\rho }}_{f}}={{\hat{U}}_{f}}{{\hat{\rho }}_{3}}{{\hat{U}}_{f}}$.

The difference in the Tsallis entropy S between the initial and final states can be bounded as follows:
\begin{equation}
\begin{aligned}
& {{S}_{q}}({{{\hat{\rho }}}_{i}})-{{S}_{q}}({{{\hat{\rho }}}_{f}}) \\
& ={{S}_{q}}({{{\hat{\rho }}}_{1}})-{{S}_{q}}({{{\hat{\rho }}}_{3}}) \\
& \le {{S}_{q}}({{{\hat{\rho }}}_{1}})-\sum\limits_{k}{{{p}_{k}}}{{S}_{q}}(\hat{\rho }_{3}^{(k)}) \\
& ={{S}_{q}}({{{\hat{\rho }}}_{1}})-\sum\limits_{k}{{{p}_{k}}}{{S}_{q}}(\hat{\rho }_{2}^{(k)}) \\
& ={{S}_{q}}({{{\hat{\rho }}}_{1}})+\sum\limits_{k}{p_{k}^{1-q}tr\left( \hat{E}_{k}^{\frac{q}{2}}{{{\hat{\rho }}}_{1}}\hat{E}_{k}^{\frac{q}{2}}{{\ln }_{q}}\frac{\sqrt{{\hat{E}}}{{{\hat{\rho }}}_{1}}\sqrt{{\hat{E}}}}{{{p}_{k}}} \right)} \\
& ={{S}_{q}}({{{\hat{\rho }}}_{1}})+{{H}_{q}}(p)+\sum\limits_{k}{tr}\left( \hat{E}_{k}^{\frac{q}{2}}{{{\hat{\rho }}}_{1}}\hat{E}_{k}^{\frac{q}{2}}{{\ln }_{q}}\sqrt{{\hat{E}}}{{{\hat{\rho }}}_{1}}\sqrt{{\hat{E}}} \right) \\
\end{aligned}\
\end{equation}
 From the definition of
QC-mutual information [22], we obtain
\begin{equation}
{{S}_{q}}({{\hat{\rho }}_{i}})-{{S}_{q}}({{\hat{\rho }}_{f}})\le I_{q}^{QC}\
\end{equation}
Result by equation (17)(24)(34):
\begin{equation}
\begin{aligned}
& {\left( \sum\limits_{m}{\frac{{{{{\beta }'}}_{m}}}{{{{\bar{Z}}}_{m}}^{1-q}}{{Q}_{qm}}} \right)}/{tr(\hat\rho _{q}^{q{{B}_{1}}})...tr(\hat\rho _{q}^{q{{B}_{n}}})}\;-{\beta }'\left\{ \frac{E_{f}^{s}}{\bar{Z}_{fq}^{1-q}}-\frac{E_{i}^{s}}{\bar{Z}_{iq}^{1-q}} \right\}\le  \\
& +\beta \left\{ -\frac{1}{\bar{Z}_{fq}^{1-q}}F_{fq}^{s}tr\left( \hat\rho _{fq}^{sq} \right)+\frac{1}{\bar{Z}_{iq}^{1-q}}F_{iq}^{s}tr\left( \rho _{iq}^{sq} \right) \right\} \\
& +\beta \left\{ \frac{1}{\bar{Z}_{fq}^{1-q}}U_{fq}^{s}tr\left( \hat\rho _{fq}^{sq} \right)-\frac{1}{\bar{Z}_{iq}^{1-q}}U_{iq}^{s}tr\left( \hat\rho _{iq}^{sq} \right) \right\} \\
& {-\sum\limits_{m}{\frac{{{\beta }_{m}}}{{{{{\beta }'}}_{m}}}\left[ tr(\hat\rho _{i}^{q})-tr(\hat\rho _{f}^{q}) \right]\left( F_{mq}^{B}-U_{mq}^{B} \right)}}/{tr(\hat\rho _{q}^{q{{B}_{1}}})...tr(\hat\rho _{q}^{q{{B}_{n}}})}\; \\
& +{(1-q)\left[ {{S}_{q}}({{\rho }_{{{B}_{1}}}})...{{S}_{q}}({{\hat\rho }_{{{B}_{m}}}}) \right]\left( {{S}_{q}}(\hat\rho _{f}^{s})-{{S}_{q}}(\hat\rho _{i}^{s}) \right)}/{tr(\hat\rho _{q}^{q{{B}_{1}}})...tr(\hat\rho _{q}^{q{{B}_{n}}})}\;+I_{q}^{QC} \\
\end{aligned}\
\end{equation}
from first law thermodynamics, work extraction from system by feedback control in nonextensive statistical is given by
\begin{equation}
\begin{aligned}
& W_{ext}^{S}\le -\beta \Delta F_{q}^{s}+\beta \Delta U_{q}^{s}{-\sum\limits_{m}{\frac{{{\beta }_{m}}}{{{{{\beta }'}}_{m}}}\left[ tr(\hat\rho _{i}^{q})-tr(\hat\rho _{f}^{q}) \right]\left( F_{mq}^{B}-U_{mq}^{B} \right)}}/{tr(\hat\rho _{q}^{q{{B}_{1}}})...tr\hat(\hat\rho _{q}^{q{{B}_{n}}})}\; \\
& +{(1-q)\left[ {{S}_{q}}({{\hat\rho }_{{{B}_{1}}}})...{{S}_{q}}({{\hat\rho }_{{{B}_{m}}}}) \right]\left( {{S}_{q}}(\hat\rho _{f}^{s})-{{S}_{q}}(\hat\rho _{i}^{s}) \right)}/{tr(\hat\rho _{q}^{q{{B}_{1}}})...tr(\hat\rho _{q}^{q{{B}_{n}}})}\;+I_{q}^{QC} \\
\end{aligned}
\end{equation}

\section{Erasure Process
We consider the following process for the information erasure in the presence of a
single heat bath. The pre-erasure state means the postmeasurement state, in which the memory stores the information of the measured
system. In the pre-erasure state, M stores outcome "k" with probability $p_k$.

We assume that, before the information erasure, the state of M under the condition
of "k" is in the canonical distribution ${{\hat{\rho }}_{q,k}}$, and that the total pre-erasure state of M
is given by
\begin{equation}
\hat{\rho }_{i}^{M}\equiv \sum\limits_{k}{{{p}_{k}}}\hat{\rho }_{q,k}^{M}\
\end{equation}
We also assume that the initial states of M and B are not correlated, and that the initial state of the total system is given by
\begin{equation}
\hat{\rho }_{i}^{MB}\equiv \hat{\rho }_{i}^{M}\otimes \hat{\rho }_{q,k}^{B}
\end{equation}
We consider the erasure process from $t = 0$ to $t=\tau $. During the erasure process, we change the Hamiltonian of M with a protocol which need to be independent of k.
The total Hamiltonian at time t then is given by
\begin{equation}
{{\hat{H}}^{MB}}(t)={{\hat{H}}^{M}}(t)+{{\hat{H}}^{\operatorname{int}}}(t)+{{\hat{H}}^{B}}
\end{equation}
where ${{\hat{H}}^{\operatorname{int}}}(t)$ is the interaction Hamiltonian between M and B.
The time evolution of the total system from time 0 to  $\tau $ is then given by the unitary operator $\hat{U}\equiv T\exp \left( -i\int{{{{\hat{H}}}^{MB}}(t)dt} \right)$, which gives the post-erasure state of the total systems
\begin{equation}
\hat{\rho }_{f}^{MB}=\hat{U}\hat{\rho }_{i}^{MB}{{\hat{U}}^{\dagger }}\
\end{equation}
We now derive the minimal energy cost that is needed for the erasure process.
From the general second law (17), we obtain
\begin{equation}
\begin{aligned}
& \left( {{S}_{q}}(\rho _{f}^{M})-{{S}_{q}}(\rho _{i}^{M}) \right)tr(\rho _{q}^{qB})\ge  \\
& \frac{{{\beta }'}}{\bar{Z}_{B}^{1-q}}Q_{eras}^{M}+\frac{\beta }{{{\beta }'}}\left[ tr(\rho _{i}^{qM})-tr(\rho _{f}^{qM}) \right]\left( F_{q}^{B}-U_{q}^{B} \right) \\
& +(1-q)\left( {{S}_{q}}(\rho _{q}^{B}) \right)\left( {{S}_{q}}(\rho _{f}^{M})-{{S}_{q}}(\rho _{i}^{M}) \right) \\
\end{aligned}
\end{equation
where $Q_{eras}^{M}=\left[ tr\left( \rho _{i}^{qMB}{\hat{H}^{B}} \right)-tr\left( \rho _{f}^{qMB}{\hat{H}^{B}} \right) \right]$ is the heat that is absorbed in M during the erasure process. On the other hand, ${{S}_{q}}\left( \hat{\rho }_{i}^{M} \right)$ can be decomposed as
\begin{equation}
\begin{aligned}
& {{S}_{q}}\left( \hat{\rho }_{i}^{M} \right)\equiv tr(\hat{\rho }_{q,k}^{Mq}){\hat{H}_{q}}(p)+\sum\limits_{k}{p_{k}^{q}{{S}_{q}}(\hat{\rho }_{q,k}^{M})} \\
& +\sum\limits_{k}{p_{k}^{q}(1-q)({{\ln }_{q}}p_{k}){{S}_{q}}(\hat{\rho }_{q,k}^{M})} \\
\end{aligned}
\end{equation}
if the conditional canonical distribution under the
condition of outcome "k" is given by
\begin{equation}
\rho _{q,k}^{M}=\frac{e_{q}^{-{\beta }'\hat{H}_{k}^{M}}}{{{{\bar{Z}}}_{q,k}}}
\end{equation}
we note that
\begin{equation}
\begin{aligned}
& {{S}_{q}}\left( \hat{\rho }_{q,}^{M} \right)\equiv \frac{{{\beta }'}}{\bar{Z}_{q}^{1-q}}E_{k}^{M}-\frac{\beta }{\bar{Z}_{q}^{1-q}}F_{k}^{M}tr(\hat{\rho }_{q,k}^{Mq}) \\
& +\frac{\beta }{\bar{Z}_{q}^{1-q}}U_{k}^{M}tr(\hat{\rho }_{q,k}^{Mq}) \\
\end{aligned}
\end{equation}
holds. On the other hand, from Klein's inequality, we have
\begin{equation}
\begin{aligned}
& {{S}_{q}}\left( \hat{\rho }_{f}^{M} \right)\le -tr(\hat{\rho }_{f}^{Mq}\ln \hat{\rho }_{q,0}^{M})=\frac{{{\beta }'}}{\bar{Z}_{q}^{1-q}}E_{0}^{M}-\frac{\beta }{\bar{Z}_{q}^{1-q}}F_{0}^{M}tr(\hat{\rho }_{f}^{M}) \\
& +\frac{\beta }{\bar{Z}_{q}^{1-q}}U_{0}^{M}tr(\hat{\rho }_{f}^{M}) \\
\end{aligned}
\end{equation}
where
\begin{equation}
E_{k}^{M}=tr(\hat{\rho }_{q,k}^{Mq}\hat{H}_{k}^{M})\
\end{equation}
and
\begin{equation}
E_{0}^{M}=tr(\hat{\rho }_{f}^{Mq}\hat{H}_{0}^{M})\
\end{equation}
are the internal energies of M. now from equations (41)(42)(44)(45) we obtain
\begin{equation}
\begin{aligned}
& \frac{{{\beta }'}}{\bar{Z}_{q}^{1-q}}\Delta E_{eras}^{M}-\frac{\beta }{\bar{Z}_{q}^{1-q}}\Delta F_{eras}^{M}+\frac{\beta }{\bar{Z}_{q}^{1-q}}\Delta U_{q}^{M} \\
& -tr(\hat{\rho }_{q,k}^{Mq}){{H}_{q}}(p)-\sum\limits_{k}{p_{k}^{q}(1-q)({{\ln }_{q}}p_{k}){{S}_{q}}(\hat{\rho }_{q,k}^{M})}\ge  \\
& \frac{1}{tr(\hat{\rho }_{q}^{qB})}\left\{ \frac{{{\beta }'}}{\bar{Z}_{B}^{1-q}}Q_{eras}^{M}+\frac{\beta }{{{\beta }'}}\left[ tr(\rho _{i}^{qM})-tr(\rho _{f}^{qM}) \right]\left( F_{q}^{B}-U_{q}^{B} \right) \right\} \\
& +\frac{1}{tr(\hat{\rho }_{q}^{qB})}\left\{ (1-q)\left( {{S}_{q}}(\rho _{q}^{B}) \right)\left( {{S}_{q}}(\rho _{f}^{M})-{{S}_{q}}(\rho _{i}^{M}) \right) \right\} \\
\end{aligned}
\end{equation}
where
\begin{equation}
\Delta E_{eras}^{M}\equiv tr(\hat{\rho }_{f}^{Mq}H_{0}^{M})-\sum\limits_{k}{{{p}_{k}}tr(\hat{\rho }_{q,k}^{Mq}H_{k}^{M})}
\end{equation}
is the difference of the averaged internal energies of M, and
\begin{equation}
\Delta F_{eras}^{M}\equiv F_{0}^{M}tr(\hat{\rho }_{f}^{qM})-\sum\limits_{k}{p_{k}^{q}F_{k}^{M}tr(\hat{\rho }_{q,k}^{Mq})}
\end{equation}
is the difference of the averaged free energies of M. therefore From the first law of thermodynamics we obtain
\begin{equation}
\begin{aligned}
& W_{eras}^{M}\ge tr(\hat{\rho }_{q,k}^{Mq}){{H}_{q}}(p)+\frac{\beta }{\bar{Z}_{q}^{M\left( 1-q \right)}}\Delta F_{eras}^{M}-\frac{\beta }{\bar{Z}_{q}^{M\left( 1-q \right)}}\Delta U_{q}^{M} \\
& +\sum\limits_{k}{p_{k}^{q}(1-q)({{\ln }_{q}}{{p}_{k}}){{S}_{q}}(\hat{\rho }_{q,can,k}^{M})} \\
& +\frac{1}{tr(\hat{\rho }_{q}^{qB})}\left\{ \frac{\beta }{{{\beta }'}}\left[ tr(\rho _{i}^{qM})-tr(\rho _{f}^{qM}) \right]\left( F_{q}^{B}-U_{q}^{B} \right) \right\} \\
& +\frac{1}{tr(\hat{\rho }_{q}^{qB})}\left\{ (1-q)\left( {{S}_{q}}(\rho _{q}^{B}) \right)\left( {{S}_{q}}(\rho _{f}^{M})-{{S}_{q}}(\rho _{i}^{M}) \right) \right\} \\
\end{aligned}
\end{equation}
\section{Measurement Process}
We next consider the measurement processes. Suppose that memory M performs
a measurement on a measured system S, and stores outcome "k" with probability
$p_k$. We assume that the memory is in contact with heat bath $B_M$. On the other hand, during the measurement, measured system S adiabatically evolves or is in contact with a different heat bath, denoted as $B_S$, which
is different from $B_M$. The latter assumption corresponds to the condition that the thermal noises on M and S are independent. The total Hamiltonian is then given by
\begin{equation}
{{\hat{H}}^{tot}}(t)={{\hat{H}}^{M}}(t)+{{\hat{H}}^{M{{B}_{M}}}}(t)+{{\hat{H}}^{{{B}_{M}}}}+{{\hat{H}}^{S}}(t)+{{\hat{H}}^{S{{B}_{S}}}}(t)+{{\hat{H}}^{{{B}_{S}}}}(t)+{{\hat{H}}^{MS}}(t)
\end{equation}
Step 1: Initial state. The initial state of M is in the standard state "0"; we assume
that the initial state of M is the conditional canonical distribution under the condition that the support of the density operator is in $H_{0}^{M}$ .Then the initial density operator of the total system is given by
\begin{equation}
\hat{\rho }_{i}^{tot}=\hat{\rho }_{q,0}^{M}\otimes \hat{\rho }_{q}^{{{B}_{M}}}\otimes {{\hat{\rho }}^{S{{B}_{s}}}}
\end{equation}
Step 2: Unitary evolution. The total system evolves unitarily due to the Hamiltonian. We write
\begin{equation}
{{\hat{U}}_{i}}\equiv T\exp \left( -i\int\limits_{0}^{{{t}_{1}}}{{{{\hat{H}}}^{tot}}(t)dt} \right)
\end{equation}
By this interaction, memory M becomes entangled with measured system S. After
this interaction, the total density operator is given by ${{\hat{U}}_{i}}\hat{\rho }_{i}^{tot}\hat{U}_{i}^{\dagger }$.
We assume that the post-measurement state is given by
\begin{equation}
\hat{\rho }_{f}^{tot}=\sum\limits_{k}{{{{\hat{M}}}_{k}}\hat{\rho }_{i}^{S{{B}_{S}}}\hat{M}_{k}^{\dagger }\otimes }\hat{\rho }_{k}^{M{{B}_{M}}}
\end{equation}
where ${{\hat{M}}_{k}}$ are the measurement operators, and $\hat{\rho }_{k}^{M{{B}_{M}}}$ are the density operators
of M and BM that are mutually orthogonal. Assumption (55) is equivalent to the assumption that any element of the POVM is given by a single measurement operator:
\begin{equation}
{{\hat{E}}_{k}}\equiv \hat{M}_{k}^{\dagger }{{\hat{M}}_{k}}
\end{equation}
Tsallis entropy is invariant under unitary evolutions and increases under projections, we have
\begin{equation}
{{S}_{q}}(\hat{\rho }_{i}^{tot})\le {{S}_{q}}(\hat{\rho }_{f}^{tot})
\end{equation}
On the other hand
\begin{equation}
\begin{aligned}
& {{S}_{q}}(\hat{\rho }_{f}^{tot})=-tr(\hat{\rho }_{k}^{qM{{B}_{M}}})H({{p}_{k}})-\sum\limits_{k}{tr(\hat{\rho }_{k}^{qM{{B}_{M}}})tr(\hat{E}_{k}^{\frac{q}{2}}\hat{\rho }_{i}^{qS{{B}_{S}}}\hat{E}_{k}^{\frac{q}{2}}{{\ln }_{q}}\sqrt{{{{\hat{E}}}_{k}}}\hat{\rho }_{i}^{qS{{B}_{S}}}\sqrt{{{{\hat{E}}}_{k}}})} \\
& +tr(\hat{\rho }_{k}^{qM{{B}_{M}}})H({{p}_{k}})+\sum\limits_{k}{p_{k}^{q}{{S}_{q}}(\hat{\rho }_{k}^{M{{B}_{M}}})}+(1-q)\sum\limits_{k}{{{S}_{q}}({{{\hat{M}}}_{k}}\hat{\rho }_{i}^{S{{B}_{S}}}\hat{M}_{k}^{\dagger }){{S}_{q}}(\hat{\rho }_{k}^{M{{B}_{M}}})} \\
\end{aligned}
\end{equation}
and
\begin{equation}
\begin{aligned}
& {{S}_{q}}(\hat{\rho }_{i}^{tot})={{S}_{q}}(\hat{\rho }_{q,0}^{M})tr(\hat{\rho }_{q}^{q{{B}_{M}}})tr({{{\hat{\rho }}}^{qS{{B}_{S}}}}) \\
& +{{S}_{q}}(\hat{\rho }_{q}^{{{B}_{M}}})tr(\hat{\rho }_{q,0}^{qM})tr({{{\hat{\rho }}}^{qS{{B}_{S}}}})+{{S}_{q}}({{{\hat{\rho }}}^{qS{{B}_{S}}}})tr(\hat{\rho }_{q}^{qM{{B}_{M}}}) \\
& +(1-q)\left[ {{S}_{q}}(\hat{\rho }_{q,0}^{M}){{S}_{q}}(\hat{\rho }_{q}^{{{B}_{M}}})tr({{{\hat{\rho }}}^{qS{{B}_{S}}}})+{{S}_{q}}(\hat{\rho }_{q}^{M{{B}_{M}}}){{S}_{q}}({{{\hat{\rho }}}^{S{{B}_{S}}}}) \right] \\
\end{aligned}
\end{equation}
From the definition of the QC-mutual information content and equation (58)(59), we obtain
\begin{equation}
\begin{aligned}
& \sum\limits_{k}{p_{k}^{q}{{S}_{q}}(\hat{\rho }_{k}^{M{{B}_{M}}})}-{{S}_{q}}(\hat{\rho }_{q,0}^{M})tr(\hat{\rho }_{q}^{q{{B}_{M}}})tr({{{\hat{\rho }}}^{qS{{B}_{S}}}}) \\
& +{{S}_{q}}(\hat{\rho }_{q}^{{{B}_{M}}})tr(\hat{\rho }_{q,0}^{qM})tr({{{\hat{\rho }}}^{qS{{B}_{S}}}})+(1-q)\left[ {{S}_{q}}(\hat{\rho }_{q,0}^{M}){{S}_{q}}(\hat{\rho }_{q}^{{{B}_{M}}})tr({{{\hat{\rho }}}^{qS{{B}_{S}}}}) \right] \\
& +(1-q)\left[ {{S}_{q}}(\hat{\rho }_{q}^{M{{B}_{M}}}){{S}_{q}}({{{\hat{\rho }}}^{S{{B}_{S}}}}) \right]+(1-q)\sum\limits_{k}{{{S}_{q}}({{{\hat{M}}}_{k}}\hat{\rho }_{i}^{S{{B}_{S}}}\hat{M}_{k}^{\dagger }){{S}_{q}}(\hat{\rho }_{k}^{M{{B}_{M}}})} \\
& \ge {I_{q}^{QC} }-tr(\hat{\rho }_{k}^{qM{{B}_{M}}})H({{p}_{k}}) \\
\end{aligned}
\end{equation}
By using Klein's inequality, we have
\begin{equation}
\begin{aligned}
& -\sum\limits_{k}{p_{k}^{q}tr(\hat{\rho }_{k}^{M{{B}_{M}}}{{\ln }_{q}}\hat{\rho }_{k}^{M}\otimes \hat{\rho }_{q}^{{{B}_{M}}})}-{{S}_{q}}(\hat{\rho }_{q,0}^{M})tr(\hat{\rho }_{q}^{q{{B}_{M}}})tr({{{\hat{\rho }}}^{qS{{B}_{S}}}}) \\
& +{{S}_{q}}(\hat{\rho }_{q}^{{{B}_{M}}})tr(\hat{\rho }_{q,0}^{qM})tr({{{\hat{\rho }}}^{qS{{B}_{S}}}})+(1-q)\left[ {{S}_{q}}(\hat{\rho }_{q,0}^{M}){{S}_{q}}(\hat{\rho }_{q}^{{{B}_{M}}})tr({{{\hat{\rho }}}^{qS{{B}_{S}}}}) \right] \\
& +(1-q)\left[ {{S}_{q}}(\hat{\rho }_{q}^{M{{B}_{M}}}){{S}_{q}}({{{\hat{\rho }}}^{S{{B}_{S}}}}) \right]+(1-q)\sum\limits_{k}{{{S}_{q}}({{{\hat{M}}}_{k}}\hat{\rho }_{i}^{S{{B}_{S}}}\hat{M}_{k}^{\dagger }){{S}_{q}}(\hat{\rho }_{k}^{M{{B}_{M}}})} \\
& \ge {I_{q}^{QC} }-tr(\hat{\rho }_{k}^{qM{{B}_{M}}})H({{p}_{k}}) \\
\end{aligned}
\end{equation}
We define the change in the averaged free energy due to the measurement as
\begin{equation}
\Delta F_{meas}^{M}\equiv \sum\limits_{k}{p_{k}^{q}F_{k}^{M}tr(\hat{\rho }_{q,k}^{qM{{B}_{M}}})}-F_{0}^{M}tr(\hat{\rho }_{q,0}^{qM})
\end{equation}
On the other hand, the ensemble average of
work performed on M during the measurement as
\begin{equation}
\begin{aligned}
& W_{meas}^{M}\equiv \sum\limits_{k}{p_{k}^{q}\left[ \frac{{{\beta }'}}{Z_{k}^{M(1-q)}}tr(\rho _{k}^{qM{{B}_{M}}}H_{k}^{M})+\frac{{{\beta }'}}{{{Z}^{B(1-q)}}}tr({{\rho }^{qM{{B}_{M}}}}{{H}^{{{B}_{M}}}}) \right]} \\
& -\left[ \frac{{{\beta }'}}{Z_{0}^{M(1-q)}}tr(\rho _{q,0}^{qM}H_{0}^{M})+\frac{{{\beta }'}}{{{Z}^{B(1-q)}}}tr(\rho _{q}^{q{{B}_{M}}}{{H}^{{{B}_{M}}}}) \right] \\
\end{aligned}
\end{equation}
we finally obtain
\begin{equation}
\begin{aligned}
& W_{meas}^{M}\ge \frac{\beta }{\bar{Z}_{q}^{M(1-q)}}\Delta F_{meas}^{M}-\frac{\beta }{\bar{Z}_{q}^{M\left( 1-q \right)}}\Delta U_{q}^{M} \\
& +\sum\limits_{k}{(1-q)tr(\hat{\rho }_{k}^{qM{{B}_{M}}})({{\ln }_{q}}\hat{\rho }_{q,k}^{M})({{\ln }_{q}}\hat{\rho }_{q}^{{{B}_{M}}})} \\
& +(1-q)\left[ {{S}_{q}}(\hat{\rho }_{q,0}^{M}){{S}_{q}}(\hat{\rho }_{q}^{{{B}_{M}}})tr({{{\hat{\rho }}}^{qS{{B}_{S}}}}) \right] \\
& +(1-q)\left[ {{S}_{q}}(\hat{\rho }_{q}^{M{{B}_{M}}}){{S}_{q}}({{{\hat{\rho }}}^{S{{B}_{S}}}}) \right] \\
& +(1-q)\sum\limits_{k}{{{S}_{q}}({{{\hat{M}}}_{k}}\hat{\rho }_{i}^{S{{B}_{S}}}\hat{M}_{k}^{\dagger }){{S}_{q}}(\hat{\rho }_{k}^{M{{B}_{M}}})} \\
& +{I_{q}^{QC} }-tr(\hat{\rho }_{k}^{qM{{B}_{M}}})H({{p}_{k}}) \\
\end{aligned}
\end{equation}
In particular, if the free-energy difference
$\Delta {{F}^{S}}$ of the controlled system S is zero By summing up inequalities (36)(51) and (64), we obtain
\begin{equation}
\begin{aligned}
& W_{ext}^{SM}\equiv W_{ext}^{S}-W_{meas}^{M}-W_{eras}^{M}\le  \\
& {-\sum\limits_{m}{\frac{{{\beta }_{m}}}{{{{{\beta }'}}_{m}}}\left[ tr(\rho _{i}^{q})-tr(\rho _{f}^{q}) \right]\left( F_{mq}^{B}-U_{mq}^{B} \right)}}/{tr(\rho _{q}^{q{{B}_{1}}})...tr(\rho _{q}^{q{{B}_{n}}})}\; \\
& +{(1-q)\left[ {{S}_{q}}({{\rho }_{{{B}_{1}}}})...{{S}_{q}}({{\rho }_{{{B}_{m}}}}) \right]\left( {{S}_{q}}(\rho _{f}^{s})-{{S}_{q}}(\rho _{i}^{s}) \right)}/{tr(\rho _{q}^{q{{B}_{1}}})...tr(\rho _{q}^{q{{B}_{n}}})}\; \\
& -\sum\limits_{k}{p_{k}^{q}(1-q)({{\ln }_{q}}{{p}_{k}}){{S}_{q}}(\hat{\rho }_{q,can,k}^{M})} \\
& -\frac{1}{tr(\hat{\rho }_{q}^{qB})}\left\{ \frac{\beta }{{{\beta }'}}\left[ tr(\rho _{i}^{qM})-tr(\rho _{f}^{qM}) \right]\left( F_{q}^{B}-U_{q}^{B} \right) \right\} \\
& -\frac{1}{tr(\hat{\rho }_{q}^{qB})}\left\{ +(1-q)\left( {{S}_{q}}(\rho _{q}^{B}) \right)\left( {{S}_{q}}(\rho _{f}^{M})-{{S}_{q}}(\rho _{i}^{M}) \right) \right\} \\
& -\sum\limits_{k}{(1-q)tr(\hat{\rho }_{k}^{qM{{B}_{M}}})({{\ln }_{q}}\hat{\rho }_{q,k}^{M})({{\ln }_{q}}\hat{\rho }_{q}^{{{B}_{M}}})} \\
& -(1-q)\left[ {{S}_{q}}(\hat{\rho }_{q,0}^{M}){{S}_{q}}(\hat{\rho }_{q}^{{{B}_{M}}})tr({{{\hat{\rho }}}^{qS{{B}_{S}}}}) \right] \\
& -(1-q)\left[ {{S}_{q}}(\hat{\rho }_{q}^{M{{B}_{M}}}){{S}_{q}}({{{\hat{\rho }}}^{S{{B}_{S}}}}) \right] \\
& -(1-q)\sum\limits_{k}{{{S}_{q}}({{{\hat{M}}}_{k}}\hat{\rho }_{i}^{S{{B}_{S}}}\hat{M}_{k}^{\dagger }){{S}_{q}}(\hat{\rho }_{k}^{M{{B}_{M}}})} \\
\end{aligned}
\end{equation}
which implies that the work that can be extracted from the total system of S and M cannot be positive. Therefore, the conventional second law of thermodynamics is satisfied for the total system.

\section{CONCLUSION}
The QC-mutual information introduced in section 5 characterizes the upper bound of the additional work that can be extracted from heat engines with the assistance of feedback control, or Maxwell's demon. By using the general results in section 6 and 7, we can essentially reconcile
Maxwell's demon with the second law of thermodynamics, which leads to a novel and general physical picture of the resolution of the paradox of Maxwell's demon.
Moreover, our results in section 6 and 7 can be regarded as the generalizations of the second law of thermodynamics to information processing processes: feedback, measurement, and information erasure.

redpajama_set_name: RedPajamaArXiv


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text:
What Is The Human Microbiome?
By Courtney Donnelly
The Urban Monk – The Human Microbiome and Health with Guest Robert Rountree
Metagenomic Testing
We are learning that there are more microbes out there in the world than we ever though could be possible. And Robert Rountree who does a lot of work for the Institute for Functional Medicine is one of the experts lifting the veil off of this topic and finding that we are swimming in them. There are organisms out there that we never even knew existed and finding out that they can do some very special things for our environment and our health.
And one really big step forward is metagenomic testing which gets down to the genetic expression of a strain of bacteria. There used to be the understanding that E.coli stood for bad bacteria because it meant there was fecal contamination involved. But now Robert says there's actually a whole range of E.coli bacteria and some of it actually happens to be beneficial to us, not toxic. This revolutionary step forward has helped new discoveries when it comes to environmental toxins. 50 % of all the detoxification of what we eat takes place in our gut by the gut microbes. Robert says this is a huge finding because of of all the studies that have been done on the liver and how it breaks it all down…that's only a small fraction of what is really going on in our bodies.
Stress and the gut
In pretty basic terms, eating healthy good foods turn on the good genes in your gut and eating bad, unhealthy foods turn on the bad genes. And stress is a big factor in also turning on the bad genes in the microbiome. If we aren't activating the "good" genes in our foods that create the enzymes that break it all down…that leads to indigestion. And Robert says that chronic indigestion turns into inflammation in the gut. Then this situation starts making you feel bad because your immune cells produce these cells called cytokines that go into systemic circulation and tell the brain that you are unwell.
There's also some crazy news that shows that these genes produce neurotransmitters that proves that things like serotonin is also being made outside the brain…they are made in neurons in the gut. Which means, bacteria is what is helping this along. This finding brings some major light on how we are treating mental illness like depression and anxiety. Perhaps these drugs like Prozac aren't doing what we thought they were, they could be working on the gut and not the brain like we think it is.
Eating Organic
The bottom line, antibiotics are killing our gut bacteria because it's decreasing the diversity of microbiome. And turns out, even if you aren't actually taking a prescription from the doctor, if you are eating meat that wasn't organically raised, there's a good chance that there are antibiotic residue in that meat. Fast food, yup, you're probably eating antibiotic residue. There's a chemical called glyphosate, which is the active ingredient in Roundup which is used all over and it's pretty common in our foods. This chemical is actually an antibiotic. It used to be sprayed on GMO crops. They are finding this in beer and wine.
The one sure way to avoid reducing your exposure to these chemicals and antibiotics is to eat organic. It's not to say that you will 100% avoid it but you will dramatically decrease your exposure to it. Another thing to help the gut is eating fermented foods like kombucha and homemade sauerkraut because it has live organisms. And of course, there's probiotics that help with maintaining a healthy gut.
Notes from the show:
Pedram:
I know there's been a lot of new technologies that have really come up that are exciting. The microbiome is really, it's got the promise but it's also very wild, wild west. There's so much we don't know. Now, with some of this next generation sequencing and all that, what are we learning?
We're learning how many more microbes are out there than we ever would have imagined. I worked my way through college studying in a microlab setting up culture plates. Basically, the option we had then was you would swab a surface, either the body or a table in the kitchen or a toilet seat and see what grew, and what grew was based on the culture media. Now we don't need a culture media. All we need is a little piece of DNA. You got the DNA, you can find out what's there.
What's happening is scientists are now going everywhere. They're going to airplanes and swabbing the trays in front of the seat to see what's growing there. There's basically this huge expedition. There's people dropping out of the sky in remote parts of the Amazon and culturing the tribes that they meet. Somebody told me this just yesterday. There was a study where they were looking at the DNA of breast milk of bears, of grizzly bears so they're [just devizing 00:01:31] the bear then sampling the breast milk of the grizzly bear and then doing this DNA analysis.
What we're finding is this incredible richness of microbes everywhere we look. Howard Hughes was all paranoid about the fact that there might be a handful of errant germs here or there on the doorknob. He couldn't even begin to imagine what we're really dealing with. We're swimming in a sea of microbes.
In the old days, we'd have little microscope and you get a little plate and then you'd look at all the bugs doing their thing and you'd be like, "Well, because I studied this, that one was that one and pathology says this one is this one." They're just so damn many and there's so much variety and our ability to now be able to sequence and just know this in a match more efficient way is opening up a lot, but what like a practical use is there in knowing this in terms of medicinal? Are we finding organisms that do very special things that we didn't know ever existed. It's like a huge salad bar in there.
The big thing that's coming out of this is doing what's called metagenomic testing. It's to understand the genetic expression of a strain of bacteria. There is E. coli and there is E. coli. We used to have this term coliforms. E. coli stood in for fecal contamination and we intended to think, "Well, it's bad." Now we know there's this whole range of E. coli bacteria. Some of them are very toxic and dangerous and some of them are quite beneficial. Our ability to actually measure the genetic expression of an individual strain is really teaching as remarkable things about what bacteria are capable of doing.
One example that I could pick is the detoxification of not just drugs but environmental toxins. We found out that perhaps as much as 50% of the detoxification and transformation of things that you eat take place in the gut by the gut microbes. That's huge. That means all these studies we've done on the liver and how the liver transforms these compounds is only a small fraction of what's actually going on.
What's actually really good news is we get this onslaught of news that's constantly telling us about how toxic the world is and how almost impossible it is to keep up with this and our poor livers but it seems like there's this frontline defense that we can reinoculate and fix that would really put a dent in that and at least give us a fighting chance against all the stuff that's coming at us.
I think it's becoming really clear that having a healthier gut microbiome and by microbiome I basically mean everything that's in there that's microscopic. We're not just talking about bacteria. We're talking about the viruses. We're talking about worms, these little microscopic worms. We're talking about beneficial fungi. Imagine that that we tend to think fungi or yeast are always bad for you but some of them are beneficial. Then there's this whole group of microbes called Archea that seem to be, they look a lot like bacteria but they actually have different chemistry and different genetics and they're involved in breaking down our food and extracting energy from our food, extracting nutrients from our food.
It's a far cry from maybe 5, 10 years ago where people were like, "Well, I take acidophilus." It's just one of millions if not, whatever. There's so much variety in there. Is this becoming stressful? How much research needs to go into this? How many people are looking at this? It seems like there needs to be entire armies of scientists now be like, "Holy crap! You know, this is what we need to look at."
There are armies of scientists working on this. This is the hottest topic in medicine today. I think I can very easily say that. Our ability to do this what's called next generation sequencing using these highly sophisticated machines that can scan a piece of feces or a scraping of the skin in a very short period of time tell you exactly what's in there. I mean this is the ability to do this in labs all over the world has opened up amazing doors. It's really changing our whole concept of what it means to be human. I'm not exaggerating when I say that. Our whole notion of what it means to be a human being has changed as a result of the information that's coming out of this research.
Let's unpack that a little bit because this is really heavy.
We've had numbers thrown around about how [many 00:06:36] bacterial DNA is more than ours. There's all sorts of contentious estimates about how much of them versus us there are. It's really starting to move the line on who we are in the first place. [Look free 00:06:49] to unpack that a little bit more.
There's some debate about the difference in the number of cells. The estimate is that humans have somewhere around 10 trillion cells and then there's at least 100 trillion microbial cells. The idea is that there's maybe 10 times more microbial cells than human cells. Some people are contesting that a little bit. Even if they do, there's no doubt that there's still a lot more microbes than there are human cells. When you put all those microbes together, they communicate with each other. They are a living organism. If you've got 3 pounds of bacteria in your gut, they're not just hanging out randomly bouncing back and forth. They are communicating with each other actively.
It's an ecosystem.
They do form a kind of organism. It has been postulated that the bacteria in our gut actually, at least some of them, can predict when we might be more susceptible to getting sick. If we're run down and we're tired, the biofilms in our intestines and a biofilm is a collection of bacteria and other organisms that are actively communicating, they can actually start circulating substances, enzymes that allow them to invade the body and do harm. What I'm saying is they are aware, in a sense, awareness we're having, be careful how we define awareness, but they know what the overall state of being is for the person.
Then there's this whole other issue of what I mentioned, the metagenome. The metagenome is the collection of all the genes, of all the viruses and fungi and bacteria, protozoa, Archea. The estimate is that were talking about at least 3.5 million genes that are floating around in our intestines, in our sinuses, on our skin. Those things are not all turned on at the same time but they have the potential to turn on.
With environmental triggers and certain kind of scenarios, pH, all the things that happen and changing there?
Yes. Stress, if you're under stress, that turns on certain genes in the microbiome. If you eat beneficial foods that turns on good genes, if you eat unhealthy food that turns on bad genes, so there's this constant dialogue between our environment and the genetic expression of all these different strains of microbes in our gut.
To further that into this symbiotic super organism conversation is okay, so now we have an expression of genes, one way or another, however, you're packing it, whether you're eating Doritos and stressing out or eating well and hiking, those genes express for what? How does that determine the outcome of how your life starts to unfold is really, I think, the depth of what we, they actually help code who we are and who we become.
In the simplest level, the genes can make enzymes that break down our food. If you're not activating the genes to make those enzymes, you don't break down your food very well and that can lead to indigestion. You have chronic indigestion, then you end up with inflammation in your gut. You have inflammation in your gut, your immune cells produce cytokines, those cytokines then go into systemic circulation and enter the brain and make you feel bad, what's called cytokines sickness. Just on that simplest level, if you're not digesting your food properly, then it can lead to feeling unwell.
The next level up is those genes actually can code for production of neurotransmitters. I think that is mind-boggling. We have known for a long time that you can make a neurotransmitter like serotonin or GABA outside of the central nervous system. These things are just being made in the brain. They're made in neurons in the gut. It's a big leap to say, "Wait a minute. Bacteria are also making those neurotransmitters?"
Where are those guys?
Yeah, and what's influencing? What tells those bacteria when to make more serotonin or when to not make enough serotonin. That brings in the whole question about how we treat mental illness, how we treat depression and anxiety. What are those drugs doing? Maybe they're not doing what we thought they were doing. Maybe Prozac is working on the gut.
Before it even gets to the brain, it's signaling [you know 00:11:39].
[inaudible 00:11:41] and maybe we could use a probiotic to do the same thing and not have the side effects of the Prozac.
A mutual friend of ours, Tom Malterre, he said something in some interview I did with him and I've interviewed him a lot [inaudible 00:11:56] where the hell I think falls anymore. Great guy, and he was mentioning how the glyphosate has created a scenario where these genetically modified foods are deprived of tryptophan. There's some studies there that he was pointing me to and I was like, "Well, that's interesting because then if we're not having a tryptophan, we're not making the serotonin, then everyone's walking around depressed, that kinda stuff sucks."
We know that most people are walking around with decimated gut microbiota like at least the balance of it because of all of the bad foods and antibiotics and all these things. It's not what it used to be. The guy who's parachuting into the village in the Amazon taking a poop sample, they're seeing a very different type of flora and ecology, then you would [see and say 00:12:47] like a kid's gut in Detroit. What is that?
Burkina Faso.
Burkina Faso, yeah. First of all, I just want to paint that picture. People are jumping into these tribes that have never had contact with the outside world and then saying, "Well, let me get your poop."
It's the Yanomami tribe. This story I understand is that somebody was doing a flyover in that area and they saw some huts. They said, "Well, we don't know of any tribe that lives in this area that's not, it's not on a registry or anything like that." They actually flew and landed, brought in anthropologists and microbiologists and started sampling these people. I'm sure that was a big surprise to these.
They had no idea, like, "Who are these guys coming from out of the sky? And why are they so interested in our poop and our spirit and our blood and all that stuff?" What they found was just amazing. They found that these guys have many times more microbes on their skin and in their guts than we do. We can have anywhere from 500 to 1,000 different types of bacteria, yeast, other kinds of fungi. Those guys have like up to 5,000 different types of organisms.
What is that quantity start to spell out? Does that start to code for a variety and agility and adaptability. You obviously have that many more genes to draw on. You have that many more like weapons in your cache there. Is that helping them with their immunity? Is that helping them against parasites, fungi, whatever?
Here's the odd thing is that these tribes, this one particular tribe and this has also been done in places like Burkina Faso that I mentioned. These people had all kinds of parasites that we think are toxic or dangerous. They had bacteria that we think are pathogens and are dangerous. They didn't have any evidence of disease as a result of this. In fact, they couldn't find any heart disease. They couldn't find any autoimmune disease. They couldn't find cancer. It turns out that a lot of these bugs that we would consider dangerous or pathogenic may actually work with our immune system to prime the immune cells so the immune cells are, they're more robust and less likely to overreact.
The way I think about it is our immune systems evolve in a time, tens of hundreds, hundreds of thousands, maybe millions of years ago when we were swimming in the sea of microbes. Now we live in this semi-sterile environment. What that means is that all it takes is one slightly abnormal bacteria or perhaps a yeast for our immune system to get very overreacted. That overreactivity can lead to an autoimmune disease like multiple sclerosis. Our tendency is to try to find the one bug that causes rheumatoid arthritis or the one bug that causes MS. Maybe it isn't so much that it's that one bug that's so bad is the fact that our immune system hasn't had that kind of exposure that it needs. Our immune systems are naive.
Interesting. They needed a challenge.
[Immune system's need 00:16:23] is exposure. They're not getting the challenges especially not getting the challenges in the first year or two of life which is when everything is forming. We think this is what's leading to allergies, auto immunedisease, inflammatory bowel disease, maybe heart disease.
How can we fix this? I know there's been a growing movement towards like fecal transplants, taking poop and blending it up and injecting it in people after they've had lots of issues. There's been some promising data on that. I think we can all agree that just taking acidophilus isn't it really the answer and this is obviously a moving target we're trying to figure it out but what do we find in working, like for the person who did grow up in the city and had spam and Cheez-Its or whatever it is and now wants to fix it, wants to do better for their kids. How do we start looking at diversity and implementing a policy towards being a little more okay with this?
The first thing that I would say is there's some really interesting research showing that when you go for a walk by the ocean or take a walk in the forest, I know we have a mutual friend, Deanna Minich, who talks about shinrin-yoku, which is the Japanese practice of walking in the forest is kind of a meditative practice. It turns out when you walk in the forest and you smell those smells that you smell in a deep, really deep forest that's been untouched, those smells indicate that you're inhaling bacteria. You're inhaling fungi. You're actually enriching your microbiome every time we go for a walk in the woods.
That's amazing.
Similarly, one drop of seawater has about 10 million viruses in it so every drop of seawater that you inhale because it's aerosolized, you get a little bit in your mouth, you go for a swim in the ocean, you're enriching your microbiome. That's really the name of the game is what are the practices that will help you enrich your microbiome. The first thing is to avoid the things that are decreasing the diversity of the microbiome and number one is antibiotics.
Antibiotics are ubiquitous in our society. I mean even if you don't get prescribed antibiotics from the doctor, if you're eating meat that wasn't organically raised, chances are there's antibiotic residues in that. You're eating pork from a fast food place. You're getting antibiotic residues. There's no question about it. It's not just the standard antibiotics we're concerned about. You mentioned glyphosate, which is the active ingredient in Roundup. They're finding glyphosate in wine from California. They're finding it in beer from Germany. It's fairly ubiquitous in foods.
Why is that important here? Because it's an antibiotic. I don't mean hypothetical antibiotic. Monsanto patented it as an antibiotic. Before it was used to spray on GMO crops, it's initially used [to which 00:19:39] was going to be as an antibiotic.
Here's this ubiquitous chemical that kills gut bacteria. That means if you want to avoid that, you're going to have to eat organic, which is no guarantee that you're going to avoid glyphosate but at least it's going to potentially reduce the exposure. Eating organic, not taking antibiotics unless they're absolutely, absolutely necessary, pretty darn important stuff.
There's something locally that just happened where group of concerned parents petitioned our local town here in Orange County, California in Irvine, and basically said, "Listen. I keep reading all this stuff about glyphosate, glyphosate and it's not cool. So why are you spraying it all over our public parks?" They actually turned it around and got the municipality to say, "Okay. We're not gonna use it anymore." I think that that's a very important step in the right direction because even I don't buy this stuff, I'm walking around and inhaling it in urban, suburban environment and you're susceptible to those things whether or not you know it if you're within the right proximity. You can make that choice at the grocery store. You make that choice at Home Depot or the hardware store but where you walk, come on. It's just hard.
It's hard to avoid. I have to say that I had my urine tested for glyphosate levels. There's an outfit called Friends of the Earth that will do that testing. It's through the Organic Consumers Association. I was surprised to see that I had a relatively high level.
You eat clean.
I eat organic. I don't eat organic all the time. I travel and you can't avoid eating conventionally grown fruits and vegetables. You can't get away from it. I was still surprised at how high my levels were. I'm guessing that if we did widespread analysis of people all over this country, they'd be shocked to find out how much Roundup they're peeing out.
Is this something that gets lodged in, say, the fat, the bones, the brain tissue or is it something that's just like a constant throughput? If you were to stop your exposure somehow [or like 00:21:53] launching yourself into the Amazon, how long before the glyphosate is out? Does it go out?
I don't think anybody knows. I don't think we know. I think the assumption is that it's not like the [old glass 00:22:03] of organochlorine chemicals that stay in your body fat forever. I think, theoretically, if you stop eating it, you should flush it out eventually. I think it's a little bit more like organophosphates.
There are studies done on organophosphates in children show that when children switch to an organic diet, within a week they weren't organophosphate-free but the amount in their urine drop dramatically. I suspect that's true with glyphosate. The problem is that there's so many sources of exposure, it's hard to know where we're getting it. [inaudible 00:22:39]
Death by a thousand cuts.
A death by a thousand cuts.
That's tough. You make the best lifestyle decisions you can and then if you have something that is a wholesale slaughtering the gut bacteria and coming in as an antibiotic that you're trying to mitigate exposure to, I guess kind of a proactive approach to at least combating that would be to take on as much beneficial organisms as you can to keep reinoculating, so hiking and what, eating yogurt, eating sauerkraut. What can you do?
It turns out that fermented foods, we've always known they were good but it turns out they're better that we ever would have imagined. By fermented food, I don't mean sauerkraut in a jar, I mean the stuff that you make yourself. It turns out the stuff in a jar or pickles in a jar don't really have a lot of live organisms in them so you really have to do it yourself. Kombucha, it's really come back in the boat partially because of this, because it does have a lot of these live organisms in them.
That's turning out to be just as good as taking probiotics. I am a big fan of probiotics but as you mentioned, there's so many unknowns about them. Now with probiotics, we're basically talking about two major groups of bacteria: lactobacilli and bifidobacteria. Then a few that go along with that like streptococcus thermophilus that you find in yogurt. The main ones that are sold commercially are lactobacilli and bifidobacteria. They're fine but they're just not very powerful. I generally find them helpful but if a person has got a serious disease like inflammatory bowel disease, it's not enough to restore their microbiome by just using those bacteria.
There's a commercial product called VSL#3. It's got 450 billion colony forming units of bacteria total per serving. For somebody with inflammatory bowel disease, I sometimes use double the strength twice a day. We're talking 900 billion twice a day.
Lay it on.
That's a massive amount of bacteria and your average person can't really do that. That's a therapeutic level. I think that's why the whole notion of using a fecal transplant has gotten increasingly popular not just for people with Clostridium difficile [inaudible 00:25:22] which is a condition that a person gets after taking antibiotics. Very terrible, intractable condition, causing chronic diarrhea, weight loss and can even lead to death. That gets cured 90% of the time with a single fecal transplant.
There's nothing in medicine that you cure 90% of with a single intervention except for this.
It's a gross intervention and it's got the little [you 00:25:50] factor but people who do it, it changes their lives. There's a couple things I'm hearing this and one of them is I just want to point out is like acidophilus and bifidus. That's like the same way we treat fruits and vegetables, just like apples or oranges, broccoli or bell peppers, out of a plethora of vegetables that are out there and fruits that are out there. We just pick a couple because they're convenient and that's it and so [as we 00:26:14] get those bouquet you're just saying like, "Oh, here are the two flowers I'm gonna keep eating." It's like, "No. We're talking about the benefit of the bouquet." How do we get a bouquet?
I just wanted for our listeners who are just like, "What the hell are they talking about?" A fecal transplant, if you don't mind, just kind of lay out what that is because I'm sure there's some people scratching their heads right now.
First of all, you select a healthy person and often that's a relative. That would be the donor. You have a person with a chronic illness like they have this chronic C. difficile diarrhea after taking antibiotics. You find a donor that's suitable, acceptable, often a family member. That person needs to get screened for everything from HIV to chronic hepatitis, viral illnesses. You also don't want a donor who is obese because it has been shown you can transfer whatever those factors are that seem to code for obesity. You can transfer that from one individual to another. We've shown that in animals and it's happened in humans.
There was this one case of a woman who got a transplant from her daughter. At the time her daughter was not obese but right after the transplant, the daughter started gaining weight and gained a lot of weight, 100 pounds. The same thing happened to the mother. Something had shifted in the daughter's microbiome that then got transferred.
Yeah, ouch. You got to be really careful. I think that's even more than the yuck factor, a bigger concern with fecal transplants and one reason I don't just recommend it to everybody is there's the possibility you will transfer things you don't want to transfer.
The good, the bad, and the ugly.
The good, the bad, and there's the ugly. You get a fecal sample and then you filter it. You make a slurry out of it. You filter it. Some people just run it through a coffee filter and people have been known to do this at home. I wouldn't recommend it but you run it through a coffee filter and so really what all you have left is the bacteria. You just have, it's a fluid that has the bacteria and the yeast and the viruses in it but it doesn't have any of the fibers or what we think of as fecal material. Then it's usually put into an enema bag and insert it up pretty high into the person's intestines.
It's coming up the bottom not from the top, people. Don't go drinking …
Actually they've done it that way. One study, what they did is they took the samples and they freeze-dried them and put them in capsules.
The results?
Through there clean capsules and it worked just as well. You can do it from the top down but that's obviously much less pleasant than going from the bottom up. This has been a folk remedy. Veterinarians have done it. It's been around for a long time.
How common is it now? I know there's a couple of guys out of Pittsburgh that were doing it. I mean it's just starting to become a thing. I want to be clear like this isn't something like, it's not something I'm advocating and you're advocating for a very few patients obviously, but how much is this become a treatment and how deployed is it around the world?
It depends on whether you're talking about self-treatment or treatment by gastroenterologist.
I think self-treatment you were saying you're not recommending at all.
I don't recommend it but it's happening all over the place.
There are a lot of people who are desperate because they have inflammatory bowel disease or they have irritable bowel syndrome or MS or something like that. There's a lot of people that are doing this. Again, I don't recommend it because there's more ways to get into trouble than you can imagine.
What I can tell you is that when I first started lecturing on this 5 or 6 years ago, I tried to find gastroenterologists around the country that were doing it, I couldn't find any. Now it's so well-accepted because there's been articles published in mainstream medical journals showing that this is more than 90% effective. There are gastroenterologists in almost every major medical center that are doing it.
If you've got Clostridium difficile, you shouldn't have any problem finding a regional center that makes this available. If, on the other hand, you had multiple sclerosis, you're going to have a hard time finding somebody in this country that will do it. They are doing it in Europe. David Perlmutter in his book Brain Maker talks about a patient who did just that, who had multiple sclerosis, went to Europe, had a fecal transplant, and had a dramatic improvement.
The implications of this are stunning. Now the thing that, so I think about this. I'm like, "Well, my grandpa is a hundred years old. His poop is probably pretty good but he has heart disease so, you know, there's a baby in the bath water, right?" What do you do? I've also read, some places where there are psychological benefits like if you were to take the poop from the Dali Lama, all of a sudden, your anxiety goes away. I read stuff like this. I don't know how much of that is now coming up more in the literature whether it was just a passing piece but to me that's fascinating that the psyche, inner psychological state, can also be influenced by the bouquet in our guts.
I don't think that that's a gross exaggeration. I really do think that there is something to it. That doesn't mean that if the Dalai Lama was selling his poop that I would [imagine 00:32:09], I would automatically want to buy some.
He's also a little overweight.
He's a little overweight so you don't know. For that reason, some people are suggesting that we get poop from infants because they, theoretically, haven't lived long enough to pick up all the bad traits that we might transfer. I think where we're going to go with this is that we're going to come up with synthetic varieties. I believe it was at the University of Guelph in Ontario, they developed a process they called RePOOPulate. What they did is they took these little samples and they extracted out a number of strains of bacteria and regrew those strains in the lab then put them back together again. Then that's what they put in the enema bag and you know what? It worked just as well as using the kind of raw …
Fecal matter.
Sample of poop. The question we have here is: is the fecal transplant working because of a specific bacteria or a small number of beneficial bacteria or is it something about the way all those bacteria interact with each other or are we transplanting an ecosystem? That's the question we really need to answer. If it's the ecosystem, then we want to do as little processing as possible. If, on the other hand, it turns out to be one or two bacteria, then instead of having a combination of lactobacilli and bifido, we might have one called faecalibacterium prausnitzii. [We're getting 00:33:56] that. I tell you there's a lot of pharmaceutical companies are doing research on this very thing. They're saying, "Is there a bacteria that we just haven't thought of before that we should be trying?"
To me that seems like the allopathic way of trying to isolate the trees and the rocks out of the garden and missing the fact that it's the garden but who knows? I'm sure we're going to find treatments and cures for all kinds of things in that query but until the jury is out on that and until that's the case I think it's the whole salad, personally it's my sentiment.
There's something that you said that did spark something in me is people suggesting taking the poop from infants. To me, I would question the origin of that infant [and said 00:34:47] poop. An infant in the Amazon sounds a lot cleaner than an infant who's three generations deep C-sections and antibiotics and what they got through mom in the vaginal pass. I don't think all infants are born equal and there might be childhood allergies, there's autism, there's all sorts of things that we're dealing with. We're like, "What the hell's happening to the kids?" Maybe these colonies are just not kind of making it through from antiquity since we started thank you Monsanto and everyone else since we start messing with things.
Martin Blaser [who's 00:35:26] head of the Department of Medicine at NYU Langone in New York and he wrote a book called The Missing Microbes. He basically says, "You know what?" Every generation is born with fewer microbes than the one before. He says, "Well, antibiotics are a big part of that, being born by C-section, treating infants in the first year of life as if they're extremely fragile," which they are to some extent but saying, "Never go outside. Omigod, you've got a baby? Never take that baby outside of the house because he might get exposed to something."
I mean if you're born, if you're a pygmy, part of the pygmy tribe in Africa, they're handing that baby back and forth. It's all over the [place 00:36:09]. You know what I'm saying?
It's like, "Well, wait a minute." You make a really good point, like where are you going to find this perfect baby that's had just the right exposures but none of the bad exposures?
Whether or not that baby's microbiota is optimized for your genetic profile to begin with, I mean if they're in the Amazon, I don't know how [my 00:36:31] genome would interact with those bugs versus the genome of someone who grew up there for 300,000 years genetically. I don't know if we knew yet.
If you got Yanomami poop put inside of you, it may turn out that you have an inflammatory reaction to some of those parasites that are in there so I would say be really careful. There's a guy named Jeff Leach that works for the Human Gut Project and he went to Tanzania and hung out with hunter gatherers there. He was basically doing that. He was eating what they ate. He ate the raw [eye bus 00:37:03]. They'd go out and they'd shoot the animal and [they're on 00:37:09] water. It's semi-desert. They would kill the animal and the first thing they do is they take out the stomach, chop it up, and then eat it on the spot. He's like, "It's sushi stomach." Now that's the way to enrich your microbiome.
[When 00:37:30] you see that like in origins, we'd go out and see a lion would take down an antelope, they would also ingest everything. Right?
They wouldn't be like, "Ew! That's dirty." It was like almost the tonic that would help them break down all that other meat and everything. I mean, they just ate it all.
The ate the whole thing. Speaking of meat, I have to say something here because there's this big movement towards doing more ketogenic diets and paleo diets and avoiding grains and making grains the bad guy. It turns out there are studies that show that when you put people in a mostly meat diet, mostly animal protein and animal fat diet, their microbiome changes in ways that are not beneficial. They start making more toxic bacteria. The question is: if just add in a little bit of fiber, is that going to be enough? If you look at what hunter-gatherers like the Hunza tribe in Tanzania, they eat everything. They're not thinking, "We eat paleo." [crosstalk 00:38:32]
They eat what's available.
They eat what they can find and so they may go for weeks without eating any meat. They're eating roots and nuts and berries and whatever they can find so variety was really the name of the game for them. There actually found this study recently that showed that when people eat a lot of whole grains, it enriches their microbiome in a really, really beneficial way. I'm concerned that if we vilify grains and tell everyone, "You should never eat grains because they're bad for your brain," et cetera, that we may be missing something here.
Look. No grains are created equal. If you take the grains and you hybridize them and you genetically modif- not modify it but induce to get the thicker stocks and the more gluten for the flavor and all that, there's a lot of things that can be done in farming without even technically messing with the genome but you are, that over time creates a hybridized wheat that might be a little much.
A little bit.
I've looked at some of [these 00:39:38] heirloom wheat kind of strains that people go back to eating and they're fine. Right?
Yes. That would be my point. I think we do generally need a lot more fiber in our diet. If a person tries really hard to eat a high-fiber diet, they might get 20 grams of fiber. If you look at what hunter-gatherers eat, it's closer to 120 to 150 grams a day. What to us seems like a lot and I have people, have patience to come in to say, "Yeah, really off my fiber. You know, I'm eating a stock of celery every day."
That's not doing it but there's a huge amount of interest now in prebiotic foods in figuring out which foods are the best prebiotics and prebiotics I mean fibers that are fermented by our gut bacteria that actually lead to enrichment of our microbiome.
I'd like to talk about this because like Terry Wahls who had a TED Talk basically ate as much as she possibly could of vegetables everyday and she cured herself of MS. I mean she just went for it. We're talking about almost impossibly big portions of vegetables that like I look at and just like, "I don't know how the hell I would even get that down," but it became her new MO. Eventually, she started chomping this stuff. When you get good at eating vegetables, the beneficial bacteria that show up also help you break them down.
[We 00:41:15] did a lecture. We were both lecturing at an event in New York where we got to hang out a little bit. I was poking around at the back of the room listening to you. You didn't know it but you talked about some of these tribes actually having certain types of termites in their guts so like they can almost eat trees because the termites are predigesting the cellulose and the fiber. Let's talk about [crosstalk 00:41:34]
They didn't actually have the actual termite.
[What I was 00:41:36] saying is their guts were like termites.
The reason that termites can eat wood is because they have bacteria in their intestines that make cellulase. What I was saying is that I was showing a picture of a woman who was grinding grain on a big stone in Burkina Faso and I was saying: "She's eating as many bugs as she is grains." She's might be eating termites and other insects but with those insects she's getting bacteria.
The bacteria that help break down the cellulose?
Yeah. There was a fascinating study that was done of a Japanese that I was asking the question: "Why is it that Japanese people eat a lot of seaweed and can digest it very well but a lot of people in the west can't digest seaweed?" It turns out that there's marine bacteria that live on the seaweed. What they found as that people that east a lot of seaweed, they actually get genetic transfer from those bacteria of the genes that code for the enzyme. We started our conversation talking about this and that's a really specific example is that I think the enzyme is called porfiranase. They make these enzymes in their own gut. Where did they get the genes to make those enzymes? They borrowed the genes from the marine bacteria that were on the seaweed.
A big source of the bacteria and a healthy microbiome come from food and what that means is that we do want to eat food that's clean but we don't want to eat food that's sterilized.
It's hard to find.
It's hard to find. If you buy your salad greens from a farmer's market, then that's going to accomplish exactly what I'm talking about. That hasn't been triple washed and scrubbed and sprayed with chlorine and all that stuff.
We're actually in a Renaissance where we're waking up from a lot and we're learning a lot and we're rapidly applying our scientific rigor and our minds to figuring out how to fix some of the things that have gone wrong. I'm incredibly enthusiastic about the news that you're sharing and the research that's coming up out of this. It's really a wonderful, wonderful direction for healthcare, for medicine for for ecology. It carries a lot of promise.
I'm becoming a ecologist again. I was very interested in that in college and so now it's come full circle where ecology and and health care are really dovetailing. We're realizing that if the planet is not healthy, then we can't be healthy, that what's going on with our gut microbiome, this lack of diversity, the overgrowth of of bad pathogens to the exclusion of the healthy, beneficial bacteria; this is similar to what's happening all over the planet. We have to work in parallel if we were poisoning our planet with all these pesticides, with Roundup in particular, with neonicotinoids which are killing the bees. All of those affect our health. It's not just a social issue that it's a nice thing to get involved in. No, this is really affecting our health.
As above, so below. We're like the little bugs on the planet that is a bigger ecosystem and it goes up and down at scale and to a degree that we don't even understand yet. We're part of something big. We're part of something that we are just starting to understand but kind of walking with reverence and kicking it old school a little bit. It's probably better than trying to reinvent the wheel at every turn and figuring out why we're not feeling well. There's there's a lot here. I'd love to have you back on the show. This is just great. We're out of time so I'd love for you to just tell our listeners and viewers where they can find you and your work.
I put most of my attention on the Institute for Functional Medicine. I lecture in their courses regularly and that's probably the best place to track me. I also attend Integrative Health Symposium in New York every February so they can track me there. I write a column for a journal called Alternative and Complementary Therapies, ACT, that's published by Mary Ann Liebert. That's readily available. I often do interviews with people. In fact, I'd love to have you come in there for an interview sometime.
I'd be honored.
Those are the different places to track me.
Awesome. Listen. I'm a big fan of your work. Keep up the good work. There's so much coming up so if a new step bubbles up, just keep me in mind. I'd love to have you back on the show and keep this conversation going.
I'd be happy to do that.
Great. Thank you so much.
All right. Thanks, man. Take care.
antibiotics, glyphosate, good bacteria, immune cells, indigestions, microbiome, Pedram Shojai, probiotics, The Urban Monk
Courtney Donnelly
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A New Year brings new market opportunities - both Globally and in the Philippines.
In this upcoming Investment Outlook 2015 seminar, I will be discussing global market trends for 2015.
Major central banks are changing their policies as their economies move toward different paths. What trends should investors look out for in 2015? China is growing with the opening of the China A-shares market, what kind of impact will that have on investors' global portfolios? Which markets and sectors should we consider and which ones should we avoid?
How will the Philippine market stack up against other emerging markets? Which sectors and themes are worth considering for 2015?
Join me for a morning of insightful discussions on major market trends and opportunities in 2015, together with investment specialist Michael Woolley (Eastspring Investments).
This review covers an awesome session, who put us on the road to having our finances in order. We're hoping to sign up for more services a little down the road, when there's actually something for this team to manage!He was thorough and patient, spending way more time with us than we expected, helping us see where we could optimize savings and retirement planning. He helped outline our targets and did some broad planning with us - as a consultation!


What Men Want (film, 2019). A 2019 American romantic comedy film with "R" rating by Paramount Pictures. Directed by Adam Shankman. Official Trailer.
What Men Want is a 2019 American romantic comedy film directed by Adam Shankman.
What Men Want (2019) - Red Band Trailer - Paramount Pictures.
Ali Davis is a successful sports agent who is constantly boxed out by her male colleagues. She expected to be made partner at the agency she works at. However, she does not receive the title since someone did not vote for her. She begins to question what more she needs to do to succeed in a man's world, until she gains the ability to hear men's thoughts from an encounter with a psychic (Sister). With her newfound power, Ali looks to outsmart her colleagues as she races to sign the next basketball superstar (Jamal Barry), but the lengths she has to go to will put her relationship with her three best friends, office assistant and a potential new love interest to the test. Towards the end of the film Ali falls in love and finds out the consequences of her ability to hear men's thoughts.
The film What Men Want was scheduled to be released by Paramount Pictures on February 8, 2019 (United States), on March 14, 2019 (Germany) and on March 15, 2019 (United Kingdom).
The duration of the film is 117 minutes. With a budget of $20 million, the film grossed over $71.2 million.
What Men Want got average rating from critics. The audience dislikes the film either. Audiences polled by CinemaScore gave the film an average grade of "A-" on a scale ranging from A+ to F.


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Christian Cupboard Emergency Food Shelf will launch a new program on Aug. 15 to provide access to the community's excess food.
Called Wildcard Wednesday, this new initiative in coordination with area grocers and Second Harvest Heartland, gathers fresh produce, dairy and meat inventory that are beyond the grocers' business needs. Volunteers at CCEFS will receive, sort and display this community abundance at their facility and welcome anyone that wants to come in and share in the bounty.
Starting Aug. 15, the Wildcard Wednesday program will run every week from 11 a.m. to 1 p.m. at CCEFS's Oakdale facility located at 8264 Fourth St. N.
This new service is in addition to its regular service hours and food support programs. Anyone is welcome to come and select from a variety of groceries and can participate every Wednesday if they would like. The available selection of food will vary from week to week, hence the "Wildcard" aspect.


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Райт () — статистически обособленная местность, расположенная в округе Окалуса (штат Флорида, США) с населением в 21 697 человек по статистическим данным переписи 2000 года.

География
По данным Бюро переписи населения США статистически обособленная местность Райт имеет общую площадь в 14,5 квадратных километров, из которых 14,24 кв. километров занимает земля и 0,26 кв. километров — вода. Площадь водных ресурсов округа составляет 1,79 % от всей его площади.

Статистически обособленная местность Райт расположена на высоте 13 м над уровнем моря.

Демография
По данным переписи населения 2000 года в Райтe проживало 21 697 человек, 5507 семей, насчитывалось 9134 домашних хозяйств и 10 004 жилых дома. Средняя плотность населения составляла около 1496,34 человек на один квадратный километр. Расовый состав населённого пункта распределился следующим образом: 76,01 % белых, 19,03 % — чёрных или афроамериканцев, 0,59 % — коренных американцев, 3,40 % — азиатов, 0,19 % — выходцев с тихоокеанских островов, 4,24 % — представителей смешанных рас, 1,53 % — других народностей. Испаноговорящие составили 5,24 % от всех жителей статистически обособленной местности.

Из 9134 домашних хозяйств в 29,0 % воспитывали детей в возрасте до 18 лет, 42,9 % представляли собой совместно проживающие супружеские пары, в 12,7 % семей женщины проживали без мужей, 39,7 % не имели семей. 29,1 % от общего числа семей на момент переписи жили самостоятельно, при этом 7,0 % составили одинокие пожилые люди в возрасте 65 лет и старше. Средний размер домашнего хозяйства составил 2,31 человек, а средний размер семьи — 2,84 человек.

Население статистически обособленной местности по возрастному диапазону по данным переписи 2000 года распределилось следующим образом: 23,2 % — жители младше 18 лет, 12,4 % — между 18 и 24 годами, 34,1 % — от 25 до 44 лет, 20,1 % — от 45 до 64 лет и 10,2 % — в возрасте 65 лет и старше. Средний возраст жителей составил 34 года. На каждые 100 женщин в Райтe приходилось 101,1 мужчин, при этом на каждые сто женщин 18 лет и старше приходилось 99,1 мужчин также старше 18 лет.

Средний доход на одно домашнее хозяйство статистически обособленной местности составил 36 940 долларов США, а средний доход на одну семью — 43 802 доллара. При этом мужчины имели средний доход в 26 870 долларов США в год против 21 646 долларов среднегодового дохода у женщин. Доход на душу населения статистически обособленной местности составил 36 940 долларов в год. 8,4 % от всего числа семей в населённом пункте и 10,9 % от всей численности населения находилось на момент переписи населения за чертой бедности, при этом 16,2 % из них были моложе 18 лет и 7,3 % — в возрасте 65 лет и старше.

Примечания

Ссылки

Статистически обособленные местности Флориды
Статистически обособленные местности округа Окалуса

redpajama_set_name: RedPajamaWikipedia


Blends easily and the smells subtle and pleasant. But i didn't find it to cover up and even the skin tone so well. I have an oily skin and didn't find it too oily.
5.0 out of 5 starsI love this stuff!
I am sold! I have very dry skin through the winter months and this BB cream combined with the Argon Wear Argon oil is great on my face and it offers great coverage. It is a little on the darker side but it works!
Light, smooth, probally the best bb cream I have tried.