Non-Markovian work fluctuation theorem in crossed electric and magnetic fields

Non-Markovian harmonic oscillator across a magnetic field and time-dependent force fields

We study the non-Markovian Brownian motion of an electrically charged harmonic oscillator through the action of both a constant magnetic field and time-dependent force fields. The generalized Langevin equation with a friction memory kernel is used to derive the generalized phase-space Fokker-Planck equation for the harmonic oscillator in the absence and in the presence of time-dependent force fields. To achieve our goal, the characteristic function method is applied to obtain, in an accurate way, the theoretical description of the problem. We explicitly calculate the correlation and cross-correlation functions for the position and velocity vectors. We show that the relevant physics behind the theory is contained in the generalized diffusion coefficient, which accounts for the natural coupling between both the harmonic oscillator and magnetic field. Our theoretical results are compared with those previously reported in the literature.

Non-Markovian barotropic-type and Hall-type fluctuation relations in crossed electric and magnetic fields

In this paper we derive the non-Markovian barotropic-type and Hall-type fluctuation relations for noninteracting charged Brownian particles embedded in a memory heat bath and under the action of crossed electric and magnetic fields. We first obtain a more general non-Markovian fluctuation relation formulated within the context of a generalized Langevin equation with arbitrary friction memory kernel and under the action of a constant magnetic field and an arbitrary time-dependent electric field. It is shown that this fluctuation relation is related to the total amount of an effective work done on the charged particle as it is driven out of equilibrium by the applied time-dependent electric field. Both non-Markovian barotropic- and Hall-type fluctuation relations are then derived when the electric field is assumed to be also a constant vector pointing along just one axis. In the Markovian limit, we show explicitly that they reduce to the same results reported in the literature.

Generalized fluctuation theorems for classical systems

The fluctuation theorem has a very special place in the study of nonequilibrium dynamics of physical systems. The form in which it is used most extensively is the Gallavoti-Cohen fluctuation theorem which is in terms of the distribution of the work p(W)/p(-W)=exp(αW). We derive the general form of the fluctuation theorems for an arbitrary multidimensional Gaussian Markov process. Interestingly, the parameter α is by no means universal, hitherto taken for granted in the case of linear Gaussian processes. As a matter of fact, conditions under which α does become a universal parameter 1/KT are found to be rather restrictive. As an application we consider fluctuation theorems for classical cyclotron motion of an electron in a parabolic potential. The motion of the electron is described by four coupled Langevin equations and thus is nontrivial. The generalized theorems are equally valid for nonequilibrium steady states and could be especially important in the presence of anisotropic diffusion.