  Synchronized brain rhythms, associated with diverse cognitive functions, have
been observed in electrical recordings of brain activity. Neural
synchronization may be well described by using the population-averaged global
potential $V_G$ in computational neuroscience. The time-averaged fluctuation of
$V_G$ plays the role of a "thermodynamic" order parameter $\cal {O}$ used for
describing the synchrony-asynchrony transition in neural systems. Population
spike synchronization may be well visualized in the raster plot of neural
spikes. The degree of neural synchronization seen in the raster plot is well
measured in terms of a "statistical-mechanical" spike-based measure $M_s$
introduced by considering the occupation and the pacing patterns of spikes. The
global potential $V_G$ is also used to give a reference global cycle for the
calculation of $M_s$. Hence, $V_G$ becomes an important collective quantity
because it is associated with calculation of both $\cal {O}$ and $M_s$.
However, it is practically difficult to directly get $V_G$ in real experiments.
To overcome this difficulty, instead of $V_G$, we employ the instantaneous
population spike rate (IPSR) which can be obtained in experiments, and develop
realistic thermodynamic and statistical-mechanical measures, based on IPSR, to
make practical characterization of the neural synchronization in both
computational and experimental neuroscience. Particularly, more accurate
characterization of weak sparse spike synchronization can be achieved in terms
of realistic statistical-mechanical IPSR-based measure, in comparison with the
conventional measure based on $V_G$.

Neurons and Cognition;Biological Physics