Current fluctuations in stochastic systems with long-range memory

Abstract

We propose a method to calculate the large deviations of current fluctuations in a class of stochastic particle systems with history-dependent rates. Long-range temporal correlations are seen to alter the speed of the large deviation function in analogy with long-range spatial correlations in equilibrium systems. We give some illuminating examples and discuss the applicability of the Gallavotti-Cohen fluctuation theorem.

10 pages, 1 figure. v2: Minor alterations. v3: Very minor alterations for consistency with published version appearing at http://stacks.iop.org/1751-8121/42/342001

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• Nonequilibrium steady state of trapped active particles
• A framework for the direct evaluation of large deviations in non-Markovian processes
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• Anomalous scalings of fluctuations of the area swept by a Brownian particle trapped in a $|x|$ potential
• Efficient large deviation estimation based on importance sampling
• Large deviations in statistics of the convex hull of passive and active particles: A theoretical study
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• Dynamics of fluctuations in the Gaussian model with conserved dynamics
• Current fluctuations of a self-interacting diffusion on a ring
• Large deviations for correlated random variables described by a matrix product ansatz
• Accelerated first-passage dynamics in a non-Markovian feedback Ornstein--Uhlenbeck process
• Towards neural reinforcement learning for large deviations in nonequilibrium systems with memory
• Dynamics of fluctuations in the Gaussian model with dissipative Langevin Dynamics