The Second Law and Biology

Abstract

Here I discuss an idea called Maximum Caliber, which provides a useful way to frame problems of non‐equilibrium statistical mechanics. It may be particularly useful for treating small‐numbers situations, such as those that often arise in biology and in nanotech, where the numbers of particles is very small. In analogy with the way the maximization of entropy over microstates leads to the Boltzmann distribution and predictions about equilibria, maximizing a quantity that E.T. Jaynes called “Caliber” over all the possible microtrajectories leads to the dynamical laws such as Fick's law of diffusion and the mass‐action laws of chemical kinetics. The Maximum Caliber method yields dynamical distribution functions that characterize the relative probabilities of different microtrajectories, including “bad actors”, i.e., the microtrajectories that contribute net particle motion in the direction opposite to the macroflux predicted by the Second Law. A potential area of application of Maximum Caliber is modern single‐particle and few‐molecule experiments that can often observe one individual dynamical particle trajectory at a time.