Intensive thermodynamic parameters in nonequilibrium systems

TL;DR

This paper introduces intensive thermodynamic parameters (ITPs) for steady-state nonequilibrium systems with conserved quantities, providing a framework to analyze phase coexistence and contact properties without requiring detailed balance.

Contribution

It defines ITPs in a broad class of nonequilibrium systems using a statistical approach that does not rely on detailed balance, expanding the tools for nonequilibrium thermodynamics.

Findings

ITPs equalize in subsystems, aiding phase coexistence analysis

ITPs can be measured via fluctuations, offering practical measurement methods

The approach applies to models with matrix product states and general additivity

Abstract

Considering a broad class of steady-state nonequilibrium systems for which some additive quantities are conserved by the dynamics, we introduce from a statistical approach intensive thermodynamic parameters (ITPs) conjugated to the conserved quantities. This definition does not require any detailed balance relation to be fulfilled. Rather, the system has to satisfy a general additivity property, which holds in most of the models usually considered in the literature, including those described by a matrix product ansatz with finite matrices. The main property of these ITPs is to take equal values in two subsystems, making them a powerful tool to describe nonequilibrium phase coexistence, as illustrated on different models. We finally discuss the issue of the equalization of ITPs when two different systems are put into contact. This issue is closely related to the possibility of measuring the ITPs using a small auxiliary system, in the same way as temperature is measured with a thermometer, and points at one of the major difficulties of nonequilibrium statistical mechanics. In addition, an efficient alternative determination, based on the measure of fluctuations, is also proposed and illustrated.