Drazin-inverse and heat capacity for driven random walkers on the ring

Abstract

We apply single and double tree-like representations of Markov jump processes on ZN for obtaining their nonequilibrium heat capacity and for taking the diffusion limit N↑∞. 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.