The ontology of temperature in nonequilibrium systems

TL;DR

This paper explores how temperature can be defined in small nonequilibrium systems, extending classical thermodynamics concepts to situations far from equilibrium where traditional definitions do not apply.

Contribution

It introduces a generalized definition of temperature applicable to small nonequilibrium systems, demonstrating the continued validity of the regression hypothesis.

Findings

Regression hypothesis holds in small nonequilibrium systems with a generalized temperature.

Traditional temperature concepts do not apply far from equilibrium, requiring new definitions.

The generalized temperature varies depending on the manifestation within the system.

Abstract

The laws of thermodynamics provide a clear concept of the temperature for an equilibrium system in the continuum limit. Meanwhile, the equipartition theorem allows one to make a connection between the ensemble average of the kinetic energy and the uniform temperature. When a system or its environment is far from equilibrium, however, such an association does not necessarily apply. In small systems, the regression hypothesis may not even apply. Herein, we show that in small nonequilibrium systems, the regression hypothesis still holds though with a generalized definition of the temperature. The latter must now be defined for each such manifestation.