  The Price equation shows the unity between the fundamental expressions of
change in biology, in information and entropy descriptions of populations, and
in aspects of thermodynamics. The Price equation partitions the change in the
average value of a metric between two populations. A population may be composed
of organisms or particles or any members of a set to which we can assign
probabilities. A metric may be biological fitness or physical energy or the
output of an arbitrarily complicated function that assigns quantitative values
to members of the population. The first part of the Price equation describes
how directly applied forces change the probabilities assigned to members of the
population when holding constant the metrical values of the members---a fixed
metrical frame of reference. The second part describes how the metrical values
change, altering the metrical frame of reference. In canonical examples, the
direct forces balance the changing metrical frame of reference, leaving the
average or total metrical values unchanged. In biology, relative reproductive
success (fitness) remains invariant as a simple consequence of the conservation
of total probability. In physics, systems often conserve total energy.
Nonconservative metrics can be described by starting with conserved metrics,
and then studying how coordinate transformations between conserved and
nonconserved metrics alter the geometry of the dynamics and the aggregate
values of populations. From this abstract perspective, key results from
different subjects appear more simply as universal geometric principles for the
dynamics of populations subject to the constraints of particular conserved
quantities

Statistical Mechanics;Populations and Evolution