2023/10/25 by Benoit Dagallier, Dagallier, Benoit · 2 citations
Mathematics · Physics and Astronomy · #60F17 (Secondary) #82C22 #82C26 (Primary) 60J28 #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2310.16793
openalex publication_date 2023/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
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.