Nonequilibrium statistical physics beyond the ideal heat bath approximation

Important models of nonequilibrium statistical physics (NESP) are limited by a commonly used, but often unrecognized, near-equilibrium approximation. Fokker-Planck and Langevin equations, the Einstein and random-flight diffusion models, and the Schnakenberg model of biochemical networks suppose that fluctuations are due to an ideal equilibrium bath. But far from equilibrium, this perfect bath concept does not hold. A more principled approach should derive the rate fluctuations from an underlying dynamical model, rather than assuming a particular form. Here, using maximum caliber as the underlying principle, we derive corrections for NESP processes in an imperfect—but more realistic—environment, corrections which become particularly important for a system driven strongly away from equilibrium. Beyond characterizing a heat bath by the single equilibrium property of its temperature, the bath's speed and size must also be used to characterize the bath's ability to handle fast or large fluctuations.

Figure 1

Finite bath size: effect of large fluctuations. Dimensionless units are employed, and $s$ is the ratio of system heat capacity to bath heat capacity—see text for more details. (Left) Mean velocity vs driving force for $s=1/100$. (Right) Variance of velocity vs. driving force for $s=1/100$.

Figure 2

Energy flow in dynamic local bath model.

Figure 3

Finite bath speed: effects of fast system fluctuations. Dimensionless units are employed, $r$ is the ratio of system response speed to local bath response speed, and $s_L$ is the ratio of system heat capacity to local bath heat capacity—see text for more details. (Left) Mean velocity vs driving force for $r{s}_L=1/100$. (Right) Variance of velocity vs driving force for $r{s}_L=1/100$.