Entropy production in ac-calorimetry

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.