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

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 & UARR; & INFIN;. 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.& COPY; 2023 Elsevier B.V. All rights reserved.

Automated summary

In this study, the single and double tree-like representations of Markov jump processes on ZN are applied to obtain their nonequilibrium heat capacity under the diffusion limit N → ∞. The Drazin-inverse of the backward generator is graphically represented, allowing for an exact computation of an important nonequilibrium quantity (excess heat) for Markov jump processes through the combination of algebraic and graph-theoretical approaches.