A Nernst heat theorem for nonequilibrium jump processes

TL;DR

This paper explores conditions under which the steady nonequilibrium heat capacity vanishes at low temperatures in Markov jump processes, extending the Third Law of thermodynamics to nonequilibrium systems.

Contribution

It introduces a dynamic condition involving relaxation times and activity levels that ensures the nonequilibrium heat capacity approaches zero at absolute zero.

Findings

Steady nonequilibrium heat capacity vanishes with temperature under certain conditions.

A dynamic condition on relaxation times is necessary for the nonequilibrium Third Law.

The framework uses Markov jump processes with local detailed balance.

Abstract

We discuss via general arguments and examples when and why the steady nonequilibrium heat capacity vanishes with temperature. The framework is the one of Markov jump processes on finite connected graphs where the condition of local detailed balance allows to identify the heat fluxes, and where the discreteness more easily enables sufficient nondegeneracy of the stationary distribution at absolute zero, as under equilibrium. However, for the nonequilibrium extension of the Third Law, a dynamic condition is needed as well: the low-temperature dynamical activity and accessibility of the dominant state must remain sufficiently high so that relaxation times do not start to dramatically differ between different initial states. It suffices in fact that the relaxation times do not exceed the dissipation time.