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

## TL;DR

This paper uses stochastic thermodynamics to analyze entropy production and heat capacity in systems with sinusoidally varying temperature, revealing their relation to complex heat capacity components.

## Contribution

It provides exact solutions for entropy production and heat capacity in systems under oscillating temperature using Fokker-Planck equations.

## Key findings

- Entropy production is continuous due to out-of-equilibrium conditions.
- Heat capacity has real and imaginary parts related to frequency.
- Results connect dynamic heat capacity to complex heat capacity components.

## Abstract

Using the 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 to 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 an imaginary parts of the complex heat capacity.