Fluctuations and correlations in weakly asymmetric simple exclusion on a ring subject to an atypical current

Benoit Dagallier

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arXiv · 2310.16793

Fluctuations and correlations in weakly asymmetric simple exclusion on a ring subject to an atypical current

Benoit Dagallier

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Abstract

We consider the weakly asymmetric simple exclusion process on a ring, driven out of equilibrium by tilting the dynamics so as to enforce a macroscopic current of particles on a large time interval. In this current-biased dynamics, the tilt by the current makes the dynamics non-local, non homogeneous and induces long-range correlations. We compute the correlation structure in the large time, large size limit for a certain range of asymmetry and current strength, recovering heuristic results of Bodineau et al. arXiv:0807.2394. In addition, in this range of parameters, we characterise the full dynamics of fluctuations around the optimal density profile in the current-biased dynamics. The key ingredient at the microscopic scale is a precise relative entropy estimate at the level of correlations. We also discuss how to remove the (technical) restriction on the range of parameters.

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Benoit Dagallier. 2023-10-25. Fluctuations and correlations in weakly asymmetric simple exclusion on a ring subject to an atypical current. https://arxiv.org/abs/2310.16793

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