Heat capacity in nonequilibrium steady states

TL;DR

This paper extends the concept of heat capacity to nonequilibrium steady states using Markov jump processes, revealing new terms and the possibility of negative heat capacities far from equilibrium.

Contribution

It introduces a consistent way to define heat capacities in nonequilibrium systems, incorporating excess heat and work, and demonstrates their behavior through examples.

Findings

Heat capacity can be defined in nonequilibrium steady states.

An additional term related to excess work appears away from equilibrium.

Steady heat capacity can become negative far from equilibrium.

Abstract

We show how to extend the concept of heat capacity to nonequilibrium systems. The main idea is to consider the excess heat released by an already dissipative system when slowly changing the environment temperature. We take the framework of Markov jump processes to embed the specific physics of small driven systems and we demonstrate that heat capacities can be consistently defined in the quasistatic limit. Away from thermal equilibrium, an additional term appears to the usual energy-temperature response at constant volume, explicitly in terms of the excess work. In linear order around an equilibrium dynamics that extra term is an energy-driving response and it is entirely determined from local detailed balance. Examples illustrate how the steady heat capacity can become negative when far from equilibrium.