Heat capacity in nonequilibrium steady states

¹ Instituut voor Theoretische Fysica, K. U. Leuven - Celestijnenlaan 200D, B-3001 Leuven, Belgium, EU
² Institute of Physics AS CR - Na Slovance 2, CZ-18221 Prague, Czech Republic, EU
³ Faculty of Mathematics and Physics, Charles University in Prague - Ke Karlovu 3, CZ-12116 Prague, Czech Republic, EU

^a eliran.boksenbojm@fys.kuleuven.be

Received: 13 September 2011
Accepted: 6 October 2011

Abstract

We show how to extend the concept of heat capacity to nonequilibrium systems. The main idea is to consider the excess heat released by an already dissipative system when slowly changing the environment temperature. We take the framework of Markov jump processes to embed the specific physics of small driven systems and we demonstrate that heat capacities can be consistently defined in the quasistatic limit. Away from thermal equilibrium, an additional term appears to the usual energy-temperature response at constant volume, explicitly in terms of the excess work. In linear order around an equilibrium dynamics that extra term is an energy-driving response and it is entirely determined from local detailed balance. Examples illustrate how the steady heat capacity can become negative when far from equilibrium.