Detailed balance has a counterpart in non-equilibrium steady states

TL;DR

This paper explores how the principle of detailed balance extends to non-equilibrium steady states, deriving constraints on transition rates based on ergodicity and microscopic laws, which differ from equilibrium assumptions.

Contribution

It introduces a new framework for transition rates in driven steady states, grounded in ergodicity and microscopic laws, challenging traditional assumptions of detailed balance.

Findings

Constraints on transition rates analogous to detailed balance.

Non-equilibrium models must respect microscopic laws without over-describing reservoirs.

Not all stochastic equations of motion are valid in non-equilibrium steady states.

Abstract

When modelling driven steady states of matter, it is common practice either to choose transition rates arbitrarily, or to assume that the principle of detailed balance remains valid away from equilibrium. Neither of those practices is theoretically well founded. Hypothesising ergodicity constrains the transition rates in driven steady states to respect relations analogous to, but different from the equilibrium principle of detailed balance. The constraints arise from demanding that the design of any model system contains no information extraneous to the microscopic laws of motion and the macroscopic observables. This prevents over-description of the non-equilibrium reservoir, and implies that not all stochastic equations of motion are equally valid. The resulting recipe for transition rates has many features in common with equilibrium statistical mechanics.