Exact computation of heat capacities for active particles on a graph

TL;DR

This paper provides exact formulas for the nonequilibrium heat capacity of active particles on a graph, using graphical methods applicable to general Markov jump processes under local detailed balance.

Contribution

It introduces a novel graphical approach to exactly compute heat capacities for active particles in energy landscapes, extending to any Markov jump process with local detailed balance.

Findings

Exact heat capacity formulas derived for active random walks.

Method applicable to a broad class of Markov processes.

Enhances understanding of energetic properties in nonequilibrium systems.

Abstract

The notion of a nonequilibrium heat capacity is important for bio-energetics and for calorimetry of active materials more generally. It centers around the notion of excess heat or excess work dissipated during a quasistatic relaxation between different nonequilibrium conditions. We give exact results for active random walks moving in an energy landscape on a graph, based on calculations employing the matrix-tree and matrix-forest theorems. That graphical method applies to any Markov jump process under the physical condition of local detailed balance, and is not restricted to the examples given in this paper.