Exact fluctuations of nonequilibrium steady states from approximate auxiliary dynamics

Abstract

We describe a framework to significantly reduce the computational effort to evaluate large deviation functions of time integrated observables within nonequilibrium steady states. We do this by incorporating an auxiliary dynamics into trajectory based Monte Carlo calculations, through a transformation of the system's propagator using an approximate guiding function. This procedure importance samples the trajectories that most contribute to the large deviation function, mitigating the exponentially complexity of such calculations. We illustrate the method by studying driven diffusions and interacting lattice models in one and two dimensions. Our work offers an avenue to calculate large deviation functions for high dimensional systems driven far from equilibrium.

Accepted in Physical Review Letters (2018). v1: Main document: 5 pages, 3 figures. Supplementary information: 5 pages, 3 figures. v2: Main document: 5 pages, 3 figures. Supplementary information: 6 pages, 3 figures. Fixed some typos and notational inconsistencies. Expanded continuum tilted operator derivation in supplementary section

References in corpus (15)

• The large deviation approach to statistical mechanics
• Thermodynamic uncertainty relation for biomolecular processes
• Fluctuation-Dissipation: Response Theory in Statistical Physics
• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Dissipation bounds all steady-state current fluctuations
• Fluctuation theorems for stochastic dynamics
• Fluctuations and response of nonequilibrium states
• Genealogical particle analysis of rare events
• Population dynamics method with a multi-canonical feedback control
• Current large deviations for driven periodic diffusions
• Finite-Size Scaling of a First-Order Dynamical Phase Transition: Adaptive Population Dynamics and an Effective Model
• Large deviation function for entropy production in driven one-dimensional systems
• Rare behavior of growth processes via umbrella sampling of trajectories
• Importance sampling large deviations in nonequilibrium steady states. I
• Order and symmetry-breaking in the fluctuations of driven systems

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