Properties of a nonequilibrium heat bath

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 nonequilibrium steady state. Because the surrounding bath of fluid under shear is also in a nonequilibrium steady state, the system receives stochastic impulses with a nonequilibrium distribution. Those impulses no longer respect detailed balance, but are nevertheless constrained by rules. The rules in question, which are applicable to a wide subclass of driven steady states, were recently derived [R. M. L. Evans, Phys. Rev. Lett. 92, 150601 (2004); J. Phys A 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 nonequilibrium noise source such as a fluid under shear.