Fluctuation relations for a classical harmonic oscillator in an electromagnetic field

In this work, we establish some fluctuation relations for a classical two-dimensional system of independent charged harmonic oscillators in the presence of an electromagnetic field. The main fluctuation relation quantifies irreversible behavior by comparing probabilities of observing particular trajectories during forward and backward processes and is expressed in terms of the work performed by the externally time-dependent electric field when the system is driven away from equilibrium. In the absence of a harmonic force and assuming a constant electric field, our theoretical results reduce to the fluctuation relations for a classical two-dimensional system of noninteracting electrons under the influence of externally crossed electric and magnetic fields, which were recently studied [D. Roy and N. Kumar, Phys. Rev. E 78, 052102 (2008)]. Finally, by considering the dragging of the center of the harmonic trap potential given by the presence of the arbitrary time-dependent electric field, the work-fluctuation theorem and the Jarzynski equality are verified.