Entropy production and heat capacity of systems under time-dependent oscillating temperature

Using stochastic thermodynamics, we determine the entropy production and the dynamic heat capacity of systems subject to a sinusoidally time-dependent temperature, in which case the systems are permanently out of thermodynamic equilibrium, inducing a continuous generation of entropy. The systems evolve in time according to a Fokker-Planck or a Fokker-Planck-Kramers equation. Solutions of these equations, for the case of harmonic forces, are found exactly, from which the heat flux, the production of entropy, and the dynamic heat capacity are obtained as functions of the frequency of the temperature modulation. These last two quantities are shown to be related to the real and imaginary parts of the complex heat capacity.