Direct evaluation of large-deviation functions

Abstract

We introduce a numerical procedure to evaluate directly the probabilities of large deviations of physical quantities, such as current or density, that are local in time. The large-deviation functions are given in terms of the typical properties of a modified dynamics, and since they no longer involve rare events, can be evaluated efficiently and over a wider ranges of values. We illustrate the method with the current fluctuations of the Totally Asymmetric Exclusion Process and with the work distribution of a driven Lorentz gas.

Updated version, extensively revised. One new figure

References in corpus (17)

• A nonequilibrium equality for free energy differences
• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Equilibrium free energy differences from nonequilibrium measurements: a master equation approach
• Fluctuation theorem for stochastic dynamics
• Dynamical ensembles in stationary states
• The Fluctuation Theorem as a Gibbs Property
• Macroscopic fluctuation theory for stationary non equilibrium states
• Current fluctuations in non-equilibrium diffusive systems: an additivity principle
• Exact Large Deviation Function in the Asymmetric Exclusion Process
• Macroscopic current fluctuations in stochastic lattice gases
• Chaotic hypothesis: Extension of Onsager reciprocity to large fields and the chaotic hypothesis
• Entropy Production in Non-Linear, Thermally Driven Hamiltonian Systems
• Large deviation functional of the weakly asymmetric exclusion process
• Fluctuations of the Entropy Production in Anharmonic Chains
• Exact joint density-current probability function for the asymmetric exclusion process
• Exact probability function for bulk density and current in the asymmetric exclusion process

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