Entropy production theorem for a charged particle in an electromagnetic field

In this work, it is shown that the detailed fluctuation theorem for the total entropy production of a charged particle in a two-dimensional harmonic trap under the action of an electromagnetic field is valid in two physical situations. The proof of the theorem is achieved if the particle is initially distributed with a canonical distribution at equilibrium with the thermal bath. The two examined cases are the following: in the first case, the charged particle in the harmonic trap is subjected to an arbitrary time-dependent electric field; in the second one, the minimum of the harmonic trap is arbitrarily dragged by such an electric field. The theoretical framework is developed within the context of stochastic thermodynamics and the Langevin dynamics for the charged particle.