Power fluctuation theorem for a Brownian harmonic oscillator

Heat statistics in the relaxation process of the Edwards-Wilkinson elastic manifold

The stochastic thermodynamics of systems with a few degrees of freedom has been studied extensively so far. We would like to extend the study to systems with more degrees of freedom and even further-continuous fields with infinite degrees of freedom. The simplest case for a continuous stochastic field is the Edwards-Wilkinson elastic manifold. It is an exactly solvable model of which the heat statistics in the relaxation process can be calculated analytically. The cumulants require a cutoff spacing to avoid ultraviolet divergence. The scaling behavior of the heat cumulants with time and the system size as well as the large deviation rate function of the heat statistics in the large size limit is obtained.

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.

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

The validity of the transient work fluctuation theorem for a charged Brownian harmonic oscillator embedded in a non-Markovian heat bath and under the action of crossed electric and magnetic fields is investigated. The aforementioned theorem is verified to be valid within the context of the generalized Langevin equation with an arbitrary memory kernel and arbitrary dragging in the potential minimum. The fluctuation-dissipation relation of the second kind is assumed to be valid and shows that the non-Markovian stochastic dynamics associated with the particle, in the absence of the external time-dependent electric field, reaches an equilibrium state, as is precisely demanded by such a relation. The Jarzynski equality in this problem is also analyzed.

Extracting work from magnetic-field-coupled Brownian particles

Thermodynamics of the magnetic-field-coupled Brownian particles is studied. We show that in the presence of the magnetic field, work can be extracted from the reservoir even when the measurement operation and the potential change operation are applied in different spatial directions. In particular, we show that more work can be extracted if the measurements are applied in two different directions simultaneously. In all these cases, we show that the generalized second law involving the measurement information and potential change is satisfied. In addition, we show how the continuous potential change and measurement position affect the work extraction.