The vanishing of excess heat for nonequilibrium processes reaching zero ambient temperature

TL;DR

This paper extends the Third Law of Thermodynamics to nonequilibrium processes, showing that excess heat and heat capacity vanish as temperature approaches zero for certain driven Markov jump processes.

Contribution

It introduces a mathematical framework demonstrating the vanishing of excess heat in nonequilibrium systems at zero temperature, extending thermodynamic principles.

Findings

Excess heat vanishes at zero environment temperature.

Nonequilibrium heat capacity approaches zero as temperature decreases.

The proof relies on matrix-forest and matrix-tree theorems for relaxation behavior.

Abstract

We present the mathematical ingredients for an extension of the Third Law of Thermodynamics (Nernst heat postulate) to nonequilibrium processes. The central quantity is the excess heat which measures the quasistatic addition to the steady dissipative power when a parameter in the dynamics is changed slowly. We prove for a class of driven Markov jump processes that it vanishes at zero environment temperature. Furthermore, the nonequilibrium heat capacity goes to zero with temperature as well. Main ingredients in the proof are the matrix-forest theorem for the relaxation behavior of the heat flux, and the matrix-tree theorem giving the low-temperature asymptotics of the stationary probability. The main new condition for the extended Third Law requires the absence of major (low-temperature induced) delays in the relaxation to the steady dissipative structure.