Work-fluctuation theorems for a particle in an electromagnetic field

Abstract

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.

Charged Brownian particles: Kramers and Smoluchowski equations and the hydrothermodynamical picture

“…Therefore, variational principles relevant to the Brownian scheme, must go beyond entropy production considerations, and include among others, free energies, efficiency factors and power output as well [69,70] and connected to nonequilibrium fluctuation and work relations [176][177][178][179][180][181][182][183][184][185].…”

Entropy Production: Its Role in Non-Equilibrium Thermodynamics

“…Their work generalized the pioneering results by Kurchan [135] on the Gallavotti-Cohen fluctuation theorem for stochastic dynamics and the generalization of Kurchan's results for Markov processes by Lebowitz and Spohn [136]. Further generalizations of van Zon and Cohen's work for electromagnetic fields are available [137]. At about the same time other important lines of research were also explored, notably by Jarzynski on the one hand and Crooks on the other.…”

Electromagnetic gauge-freedom and work

“…(46,47) amount to the first law. Importantly, (46,47) are written in finite differences: in the relativistic situation the energy transfer does take a finite time, since the energy has to pass through the EMF. Hence (47) cannot hold for a small |t 2 − t 1 |.…”

“…1(a), 1(b) and 2(a) show that for a range of initial times E is strictly conserved. Hence (47) does not hold and no work can be defined via (46). This relates to the fact that for parameters of Figs.…”