Exact computation of heat capacities for active particles on a graph

Abstract The notion of a nonequilibrium heat capacity is important for bio-energetics and calorimetry active materials more generally. It centers around the excess or work dissipated during quasistatic relaxation between different conditions. We give exact results random walks moving in an energy landscape on graph, based calculations employing matrix-tree matrix-forest theorems. That graphical method applies to any Markov jump process under physical condition local detailed balance.