Work-fluctuation theorems for a particle in an electromagnetic field

The theoretical study about the transient and stationary fluctuation theorems is extended to include the effects of electromagnetic fields on a charged Brownian particle. In particular, we consider a harmonic trapped Brownian particle under the action of a constant magnetic field pointing perpendicular to a plane and a time-dependent electric field acting on this plane. The electric field is seen to be responsible for the motion of the center in the harmonic trap, giving as a result a time-dependent dragging. Our study is focused on the solution of the Smoluchowski equation associated with the over-damped Langevin equation and also considers two particular cases for the motion of the harmonic trap minimum. The first one is produced by a linear time-dependent electric field and, in the second case an oscillating electric field produces a circular motion. In this last case we have found resonant behavior in the mean work when the electric field is tuned with Larmor's frequency. Some comparisons are made with other works in the absence of the magnetic field.