Drazin-Inverse and heat capacity for driven random walks on the ring

Abstract

We apply single and double tree-like representations of Markov jump processes on ${\mathbb{Z}}_N$ for obtaining their nonequilibrium heat capacity and for taking the diffusion limit $N\uparrow \infty$. The main tool is a graphical representation of the Drazin-inverse of the backward generator. In that way, the combination of algebraic and graph-theoretical approaches enables an exact computation of an important nonequilibrium quantity (excess heat) for Markov jump processes.

References in corpus (8)

• Steady state statistics of driven diffusions
• Steady State Thermodynamics for Heat Conduction -- Microscopic Derivation
• Forest matrices around the Laplacian matrix
• A Nernst heat theorem for nonequilibrium jump processes
• Calorimetry for active systems
• Trees and forests for nonequilibrium purposes: an introduction to graphical representations
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• The vanishing of excess heat for nonequilibrium processes reaching zero ambient temperature

Cited by in corpus (5)

• The vanishing of excess heat for nonequilibrium processes reaching zero ambient temperature
• On the Poisson equation for nonreversible Markov jump processes
• Specific heat of a driven lattice gas
• Close-to-equilibrium heat capacity
• Negative specific heats: where Clausius and Boltzmann entropies separate