Close-to-equilibrium heat capacity

TL;DR

This paper investigates the heat capacity near equilibrium, extending the canonical ensemble formula to the McLennan regime, revealing that it always vanishes at zero temperature and that violations of the Third Law are nonlinear effects.

Contribution

It introduces an extended expression for heat capacity in the McLennan regime, generalizing the equilibrium formula to near-equilibrium conditions.

Findings

Heat capacity in the McLennan regime can be expressed via average energy.

It always vanishes at zero temperature.

Violations of the Third Law are nonlinear effects.

Abstract

Close to equilibrium, the excess heat governs the static fluctuations. We study the heat capacity in that McLennan regime, i.e., in linear order around equilibrium, using an expression in terms of the average energy that extends the equilibrium formula in the canonical ensemble. It is derivable from an entropy and it always vanishes at zero temperature. Any violation of an extended Third Law is, therefore, a nonlinear effect.