Journal ArticleDOI
Hydrodynamics and fluctuations outside of local equilibrium: Driven diffusive systems
TLDR
In this paper, the authors derived hydrodynamic equations for systems not in local thermodynamic equilibrium, that is, where the local stationary measures are non-Gibbsian and do not satisfy detailed balance with respect to the microscopic dynamics.Abstract:
We derive hydrodynamic equations for systems not in local thermodynamic equilibrium, that is, where the local stationary measures are “non-Gibbsian” and do not satisfy detailed balance with respect to the microscopic dynamics. As a main example we consider thedriven diffusive systems (DDS), such as electrical conductors in an applied field with diffusion of charge carriers. In such systems, the hydrodynamic description is provided by a nonlinear drift-diffusion equation, which we derive by a microscopic method ofnonequilibrium distributions. The formal derivation yields a Green-Kubo formula for the bulk diffusion matrix and microscopic prescriptions for the drift velocity and “nonequilibrium entropy” as functions of charge density. Properties of the hydrodynamic equations are established, including an “H-theorem” on increase of the thermodynamic potential, or “entropy”, describing approach to the homogeneous steady state. The results are shown to be consistent with the derivation of the linearized hydrodynamics for DDS by the Kadanoff-Martin correlation-function method and with rigorous results for particular models. We discuss also the internal noise in such systems, which we show to be governed by a generalizedfluctuation-dissipation relation (FDR), whose validity is not restricted to thermal equilibrium or to time-reversible systems. In the case of DDS, the FDR yields a version of a relation proposed some time ago by Price between the covariance matrix of electrical current noise and the bulk diffusion matrix of charge density. Our derivation of the hydrodynamic laws is in a form—the so-called “Onsager force-flux form” which allows us to exploit the FDR to construct the Langevin description of the fluctuations. In particular, we show that the probability of large fluctuations in the hydrodynamic histories is governed by a version of the Onsager “principle of least dissipation,” which estimates the probability of fluctuations in terms of the Ohmic dissipation required to produce them and provides a variational characterization of the most probable behavior as that associated to least (excess) dissipation. Finally, we consider the relation of longrange spatial correlations in the steady state of the DDS and the validity of ordinary hydrodynamic laws. We also discuss briefly the application of the general methods of this paper to other cases, such as reaction-diffusion systems or magnetohydrodynamics of plasmas.read more
Citations
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Journal ArticleDOI
A gallavotti-cohen-type symmetry in the large deviation functional for stochastic dynamics
Joel L. Lebowitz,Herbert Spohn +1 more
TL;DR: In this article, the authors extend the work of Kurchan on the Gallavotti-Cohen fluctuation theorem, which yields a symmetry property of the large deviation function, to general Markov processes.
Journal ArticleDOI
Fluctuation-dissipation: Response theory in statistical physics
TL;DR: In this paper, the relation between the relaxation of spontaneous fluctuations and the response to an external perturbation is discussed, and the connection of these works with large deviation theory is analyzed.
Journal ArticleDOI
Large Deviation of the Density Profile in the Steady State of the Open Symmetric Simple Exclusion Process
TL;DR: In this paper, the authors considered an open one dimensional lattice gas on sites i=1,..., N, with particles jumping independently with rate 1 to neighboring interior empty sites, the simple symmetric exclusion process, and the particle fluxes at the left and right boundaries, corresponding to exchanges with reservoirs at different chemical potentials, create a stationary nonequilibrium state (SNS) with a steady flux of particles through the system.
Journal ArticleDOI
Fourier's law for a harmonic crystal with self-consistent stochastic reservoirs
TL;DR: In this article, the authors considered a d-dimensional harmonic crystal in contact with a stochastic Langevin type heat bath at each site and proved that this requirement uniquely fixes the temperatures and the self consistent system has a unique steady state.
Journal ArticleDOI
Steady State Thermodynamics
Shin-ichi Sasa,Hal Tasaki +1 more
Abstract: The present paper reports our attempt to search for a new universal framework in nonequilibrium physics. We propose a thermodynamic formalism that is expected to apply to a large class of nonequilibrium steady states including a heat conducting fluid, a sheared fluid, and an electrically conducting fluid. We call our theory steady state thermodynamics (SST) after Oono and Paniconi's original proposal. The construction of SST is based on a careful examination of how the basic notions in thermodynamics should be modified in nonequilibrium steady states. We define all thermodynamic quantities through operational procedures which can be (in principle) realized experimentally. Based on SST thus constructed, we make some nontrivial predictions, including an extension of Einstein's formula on density fluctuation, an extension of the minimum work principle, the existence of a new osmotic pressure of a purely nonequilibrium origin, and a shift of coexistence temperature. All these predictions may be checked experimentally to test SST for its quantitative validity.
References
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TL;DR: In this article, the propagation of electromagnetic waves and X-ray diffraction of X rays in crystals are discussed. But they do not consider the effects of superconductivity on superconducting conductors.
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Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen
TL;DR: In el marco del Proyecto subvencionado by the Fundación Antorchas (FAN) as discussed by the authors, el material was digitalizado, e.g., en la Biblioteca del Departamento de Fisica de la Facultad de Ciencias Exactas de la Universidad Nacional de La Plata.
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TL;DR: The construction, and other general results are given in this paper, with values in [0, ] s. The voter model, the contact process, the nearest-particle system, and the exclusion process.
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M. I. Freĭdlin,A. D. Ventt︠s︡elʹ +1 more
TL;DR: In this article, the authors introduce the concept of random perturbations in Dynamical Systems with a Finite Time Interval (FTI) and the Averaging Principle.
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