  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.
