Non-Equilibrium Statistical Physics Beyond the Ideal Heat Bath Approximation

TL;DR

This paper develops a more realistic framework for nonequilibrium statistical physics that accounts for imperfect environments, moving beyond the ideal heat bath approximation by deriving corrections using the Maximum Caliber principle.

Contribution

It introduces a principled approach to model rate fluctuations in nonequilibrium systems without relying on the ideal heat bath assumption, incorporating bath dynamics.

Findings

Corrections are significant for systems far from equilibrium.

Bath properties like speed and size influence fluctuation handling.

Provides a more accurate modeling framework for nonequilibrium processes.

Abstract

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.