Properties of a non-equilibrium heat bath

TL;DR

This paper derives fundamental rules governing stochastic impulses in non-equilibrium steady states, extending previous work, and applies these rules to models of particles interacting through non-equilibrium noise.

Contribution

It provides a fundamental derivation of non-equilibrium impulse rules using basic probability principles, expanding understanding of driven steady states.

Findings

Impulses in non-equilibrium states do not obey detailed balance.

Derived rules constrain stochastic behavior in driven steady states.

Applied results to models showing non-equilibrium forces mediated by shear flow.

Abstract

At equilibrium, a fluid element, within a larger heat bath, receives random impulses from the bath. Those impulses, which induce stochastic transitions in the system (the fluid element), respect the principle of detailed balance, because the bath is also at equilibrium. Under continuous shear, the fluid element adopts a non-equilibrium steady state. Because the surrounding bath of fluid under shear is also in a non-equilibrium steady state, the system receives stochastic impulses with a non-equilibrium distribution. Those impulses no longer respect detailed balance, but are nevertheless constrained by rules. The rules in question, which are applicable to a wide sub-class of driven steady states, were recently derived [R. M. L. Evans, Phys. Rev. Lett. {\bf 92}, 150601 (2004); J. Phys. A: Math. Gen. {\bf 38}, 293 (2005)] using information-theoretic arguments. In the present paper, we provide a more fundamental derivation, based on the uncontroversial, non-Bayesian interpretation of probabilities as simple ratios of countable quantities. We apply the results to some simple models of interacting particles, to investigate the nature of forces that are mediated by a non-equilibrium noise-source such as a fluid under shear.