Entropy production in ac-calorimetry

TL;DR

This paper explores how ac-calorimetry measurements, which are affected by irreversible processes, can be understood through frequency-dependent complex heat capacity, linking the imaginary part to entropy production.

Contribution

It demonstrates that the imaginary component of complex heat capacity in ac-calorimetry is directly related to entropy produced during irreversible processes.

Findings

Imaginary heat capacity indicates non-equilibrium heat participation.

Complex heat capacity can be inferred for each irreversible process.

Imaginary part correlates with entropy production.

Abstract

In calorimetry and particularly in heat capacity measurements, different characteristic relaxation time constants may perturb the experiment which cannot be considered at thermodynamic equilibrium. In this case, thermodynamics of irreversible processes has to be taken into account and the calorimetric measurements must be considered as dynamic. In a temperature modulated experiment, such as ac-calorimetry, these non-equilibrium experiments give rise to the notion of frequency dependent complex heat capacity. In this paper, it is shown that for each irreversible process an experimental frequency dependent complex heat capacity can be inferred. Furthermore, we demonstrate rigorously that a same equality connects the imaginary part of these different complex heat capacities with the entropy produced during these irreversible processes. Finally, we claim that the presence of an imaginary part in the measured heat capacity always indicates that a certain amount of heat does not participate to the classical equilibrium heat capacity of the sample when measured over the observation time scale.