Non-Equilibrium Statistical Physics Beyond the Ideal Heat Bath Approximation

Jonathan Asher Pachter, Ken A. Dill

Published 2022-04-27Version 1

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 far from equilibrium. Beyond characterizing a heat bath by the single equilibrium property of temperature, we must also consider finite bath size and finite bath speed to fully describe dynamics further from equilibrium.