Representation of nonequilibrium steady states in large mechanical systems

TL;DR

This paper extends a recent concise representation of nonequilibrium steady states to classical mechanical systems with deterministic baths, covering various transport phenomena and providing a simplified derivation.

Contribution

It generalizes the representation of nonequilibrium steady states to a broad class of classical mechanical systems with deterministic reservoirs.

Findings

Representation valid for systems with heat conduction, particle flow, and oscillating fields.

Extension covers full order representation.

Simplified derivation provided.

Abstract

Recently a novel concise representation of the probability distribution of heat conducting nonequilibrium steady states was derived. The representation is valid to the second order in the ``degree of nonequilibrium'', and has a very suggestive form where the effective Hamiltonian is determined by the excess entropy production. Here we extend the representation to a wide class of nonequilibrium steady states realized in classical mechanical systems where baths (reservoirs) are also defined in terms of deterministic mechanics. The present extension covers such nonequilibrium steady states with a heat conduction, with particle flow (maintained either by external field or by particle reservoirs), and under an oscillating external field. We also simplify the derivation and discuss the corresponding representation to the full order.