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 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.

The Sun within: active processes from two-temperature models

“…Apart from that conceptual framework, which is generally useful for understanding efficiencies in active or bio-mimicking matter in material science [2], the embedding of active particle models in two-temperature processes allows the use of statistical thermodynamics For its thermal properties, the heat capacity in the McLennan ensemble was recently studied in [52]. That distribution is called after McLennan because of the introduction in [34]; see also [33].…”

“…That switch will be responsible for a nonequilibrium occupation statistics. For n = 2 we are dealing with a switch for a two-level system (or classical qubit) where at random times the ground state and the excited state get exchanged, [21, 32].…”

“…[19]. For the biological physics of population inversion as visible from calorimetry on active systems, we refer to [20,21].…”

“…[19]. For the biological physics of population inversion as visible from calorimetry on active systems, we refer to [20, 21]. Bringing these subjects together and unified under the governing body of nonequilibrium statistical mechanics is a theoretical contribution to which the present paper wishes to add.…”

Close-to-equilibrium heat capacity

“…In recent papers [4][5][6][7][8], building on suggestions from steady-state thermodynamics [9][10][11], the notion of heat capacity was generalized to driven and active systems. There, a quasipotential captures the quasistatic excess heat, [3,7,12,13], which is the analogue of energy changes under detailed balance processes.…”