Fluctuation relations and rare realizations of transport observables

Fluctuation relations establish rigorous identities for the nonequilibrium averages of observables. Starting from a general transport master equation with time-dependent rates, we employ the stochastic path integral approach to study statistical fluctuations around such averages. We show how under nonequilibrium conditions, rare realizations of transport observables are crucial and imply massive fluctuations that may completely mask such identities. Quantitative estimates for these fluctuations are provided. We illustrate our results on the paradigmatic example of a mesoscopic RC circuit.Comment: 4 pages, 3 figures; v2: minor changes, published versio

Electron and Phonon Thermal Waves in Semiconductors: an Application to Photothermal Effects

The electron and phonon temperature distribution function are calculated in semiconductors. We solved the coupled one-dimensional heat-diffussion equations in the linear approximation in which the physical parameters on the sample are independent of the temperature. We also consider the heat flux at the surface of the semiconductor as a boundary condition for each electron and phonon systems instead of using a fixed temperature. From this, we obtain an expression for electron and phonon temperature respectively. The characterization of the thermal waves properties is duscussed and some practical procedures for this purpose provide us information about the electron and phonon thermal parameters.Comment: 12 pages, amstex and amssymb macro package (LaTeX2e edition

Minimal Work Principle and its Limits for Classical Systems

The minimal work principle asserts that work done on a thermally isolated equilibrium system, is minimal for the slowest (adiabatic) realization of a given process. This principle, one of the formulations of the second law, is operationally well-defined for any finite (few particle) Hamiltonian system. Within classical Hamiltonian mechanics, we show that the principle is valid for a system of which the observable of work is an ergodic function. For non-ergodic systems the principle may or may not hold, depending on additional conditions. Examples displaying the limits of the principle are presented and their direct experimental realizations are discussed.Comment: 4 + epsilon pages, 1 figure, revte

Fluctuation theorems for stochastic dynamics

Fluctuation theorems make use of time reversal to make predictions about entropy production in many-body systems far from thermal equilibrium. Here we review the wide variety of distinct, but interconnected, relations that have been derived and investigated theoretically and experimentally. Significantly, we demonstrate, in the context of Markovian stochastic dynamics, how these different fluctuation theorems arise from a simple fundamental time-reversal symmetry of a certain class of observables. Appealing to the notion of Gibbs entropy allows for a microscopic definition of entropy production in terms of these observables. We work with the master equation approach, which leads to a mathematically straightforward proof and provides direct insight into the probabilistic meaning of the quantities involved. Finally, we point to some experiments that elucidate the practical significance of fluctuation relations.Comment: 48 pages, 2 figures. v2: minor changes for consistency with published versio

Stochastic deformation of a thermodynamic symplectic structure

A stochastic deformation of a thermodynamic symplectic structure is studied. The stochastic deformation procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an imaginary deformation parameter (the Planck constant). Gauge symmetries of thermodynamics and corresponding stochastic mechanics, which describes fluctuations of a thermodynamic system, are revealed and gauge fields are introduced. A physical interpretation to the gauge transformations and gauge fields is given. An application of the formalism to a description of systems with distributed parameters in a local thermodynamic equilibrium is considered.Comment: 22 pages, revtex preprint style; some notations changed and references added; some formulas and comments adde

Linear response theory and transient fluctuation theorems for diffusion processes: a backward point of view

On the basis of perturbed Kolmogorov backward equations and path integral representation, we unify the derivations of the linear response theory and transient fluctuation theorems for continuous diffusion processes from a backward point of view. We find that a variety of transient fluctuation theorems could be interpreted as a consequence of a generalized Chapman-Kolmogorov equation, which intrinsically arises from the Markovian characteristic of diffusion processes

Thermal Diffusion of a Two Layer System

In this paper thermal conductivity and thermal diffusivity of a two layer system is examined from the theoretical point of view. We use the one dimensional heat diffusion equation with the appropriate solution in each layer and boundary conditions at the interfaces to calculate the heat transport in this bounded system. We also consider the heat flux at the surface of the samle as boundary condition instead of using a fixed tempertaure. From this, we obtain an expression for the efective thermal diffusivity of the composite sample in terms of the thermal diffusivity of its constituent materials whithout any approximations.Comment: 16 pages, 1 figure, RevTeX v. 3.0 macro packag

Classical and Thermodynamic work fluctuations

We have studied the nature of classical work ($W_{c}$) and thermodynamic work ($W$) fluctuations in systems driven out of equilibrium both in transient and time periodic steady state. As the observation time of trajectory increases, we show that the number of trajectories which exhibit excursions away from the typical behaviour i.e., $W_{c}<0$, $W<\Delta F$ and dissipated heat $Q<0$ decreases as anticipated for macroscopic time scales. Analytical expressions for such trajectories are obtained. Trajectory for which $W_{c}<0$ may not correspond to $W<\Delta F$ or $Q<0$. The applicability of steady state fluctuation theorems are discussed in our linear as well as nonlinear models.Comment: Based on the talk presented by Mamata Sahoo at the Condensed Matter Days-Aug. 2008 held at Viswavarati University, Kolkata. 19 pages, 8 figure

Quantum Fluctuation Relations for the Lindblad Master Equation

An open quantum system interacting with its environment can be modeled under suitable assumptions as a Markov process, described by a Lindblad master equation. In this work, we derive a general set of fluctuation relations for systems governed by a Lindblad equation. These identities provide quantum versions of Jarzynski-Hatano-Sasa and Crooks relations. In the linear response regime, these fluctuation relations yield a fluctuation-dissipation theorem (FDT) valid for a stationary state arbitrarily far from equilibrium. For a closed system, this FDT reduces to the celebrated Callen-Welton-Kubo formula