Entropy: A little understood concept in physics [video]
While this is a reasonable historical explanation of entropy, and explains that we don&#x27;t gain net energy from the sun, it still misses the mark on what entropy is now known to be.<p>Entropy isn&#x27;t a property of an object, or a system or things in physics.  Entropy is a property of our _description_ of systems.  More precisely it is a measure of how poorly a given specification of a physical system is, i.e. given description of a systems, typically the pressure &#x2F; volume &#x2F; temperature of a gas or whatnot, how many different physical systems correspond to such a description.<p>In particular, _thermodynamic entropy is Shannon entropy_.<p>In the case where the description of state specifies a volume of phase space wherein a physical state lies within, then the entropy is the logarithm of the volume of this fragment of phase space.  If we take this collection of states and see how they evolve in time, then Liouville’s theorem says the volume of phase space will remain constant.<p>If we want to build a reliable machine, i.e. an engine, that can operate in any initial state that is bounded by our description, and ends up win a final state bounded by some other description, well, in order for this machine to preform reliably, the volume of the final description needs to be greater than the volume of the description of the initial state.  Otherwise, some possible initial states will fail to end up in the desired final state.  This is the essence of the second law of thermodynamics.<p>I want to emphasis this: entropy exists in our heads, not in the world.<p>E.T. Jaynes illustrated this &quot;5. The Gas Mixing Scenario Revisited&quot; in <a href="https:&#x2F;&#x2F;www.damtp.cam.ac.uk&#x2F;user&#x2F;tong&#x2F;statphys&#x2F;jaynes.pdf" rel="nofollow noreferrer">https:&#x2F;&#x2F;www.damtp.cam.ac.uk&#x2F;user&#x2F;tong&#x2F;statphys&#x2F;jaynes.pdf</a> where two imaginary variants of Argon gas are mixed together.  If one engineer is ignorant of the different variants of Argon gas, it is impossible to extract work from the gas, but armed with knowledge of the difference (which must be exploitable otherwise they wouldn&#x27;t actually be different) work can be extracted.<p>Knowledge _is_ power.<p>Taking an extreme example, suppose we have two volumes of gas at different volumes &#x2F; pressures &#x2F; temperature.  We can compute how much work can be extracted from those gases.<p>But, suppose someone else knows more than just the volume &#x2F; pressure &#x2F; temperature of these gases.  This someone happens to know the precise position and velocity of every single molecule of gas (more practically they know the quantum state of the system).  This someone now gets to play a the role of Maxwell&#x27;s demon and separate all the high velocity and low velocity molecules of each chamber, opening and closing a gate using their perfect knowledge of where each particle is at each moment in time.  From this they can now extract far more work than the ignorant person.<p>In both cases the gas was identical.  How much useful work one can extract depends on how precise one&#x27;s knowledge of the state of that gas is.