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

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.

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Cited by in corpus (6)

• Exact computation of heat capacities for active particles on a graph
• On the Poisson equation for nonreversible Markov jump processes
• Drazin-Inverse and heat capacity for driven random walks on the ring
• Exactly solvable diffusions from space-time transformations
• Close-to-equilibrium heat capacity
• Negative specific heats: where Clausius and Boltzmann entropies separate