A Nernst heat theorem for nonequilibrium jump processes

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.

Automated summary

We discuss when and why the steady nonequilibrium heat capacity vanishes with temperature using general arguments and examples. The framework of Markov jump processes on finite connected graphs is used, where the condition of local detailed balance helps identify the heat fluxes, and the discreteness enables a nondegenerate stationary distribution at absolute zero. Additionally, a dynamic condition is needed for the nonequilibrium extension of the Third Law to ensure that the low-temperature dynamical activity and accessibility of the dominant state remain sufficiently high.