Weak additivity principle for current statistics in d-dimensions

Abstract

The additivity principle (AP) allows to compute the current distribution in many one-dimensional (1d) nonequilibrium systems. Here we extend this conjecture to general d-dimensional driven diffusive systems, and validate its predictions against both numerical simulations of rare events and microscopic exact calculations of three paradigmatic models of diffusive transport in d=2. Crucially, the existence of a structured current vector field at the fluctuating level, coupled to the local mobility, turns out to be essential to understand current statistics in d>1. We prove that, when compared to the straightforward extension of the AP to high-d, the so-called weak AP always yields a better minimizer of the macroscopic fluctuation theory action for current statistics.

Main: 6 pages + 2 figs. Supplementary material: 7 pages + 4 figures

References in corpus (21)

• The large deviation approach to statistical mechanics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Fluctuation theorems for stochastic dynamics
• Large Deviations in Single File Diffusion
• A numerical approach to large deviations in continuous-time
• Hyperuniformity and phase separation in biased ensembles of trajectories for diffusive systems
• The Physicist's Companion to Current Fluctuations: One-Dimensional Bulk-Driven Lattice Gases
• Symmetries in Fluctuations Far from Equilibrium
• Mapping Nonequilibrium onto Equilibrium: The Macroscopic Fluctuations of Simple Transport Models
• Perturbative calculation of quasi-potential in non-equilibrium diffusions: a mean-field example
• Density profiles, dynamics, and condensation in the ZRP conditioned on an atypical current
• Current Fluctuations and Statistics During a Large Deviation Event in an Exactly-Solvable Transport Model
• Large Fluctuations of the Macroscopic Current in Diffusive Systems: A Confirmation of the Additivity Principle
• Survival of a static target in a gas of diffusing particles with exclusion
• Le Chatelier principle for out of equilibrium and boundary driven systems : application to dynamical phase transitions
• Anisotropic Isometric Fluctuation Relations in experiment and theory on a self-propelled rod
• Isometric fluctuation relations for equilibrium states with broken symmetry
• Large fluctuations in diffusion-controlled absorption
• Melting of an Ising Quadrant
• Local structure of current fluctuations in diffusive systems beyond one dimension
• Current fluctuations in boundary driven diffusive systems in different dimensions: a numerical study

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• Dynamical large deviations of two-dimensional kinetically constrained models using a neural-network state ansatz
• Dynamical criticality in open systems: non-perturbative physics, microscopic origin and direct observation
• Symmetry-induced fluctuation relations for dynamical observables irrespective of their behaviour under time-reversal
• Dynamical phase transition to localized states in the two-dimensional random walk conditioned on partial currents
• Density large deviations for multidimensional stochastic hyperbolic conservation laws
• Large deviations of current for the symmetric simple exclusion process on a semi-infinite line, and on an infinite line with a slow bond
• Infinite family of universal profiles for heat current statistics in Fourier's law
• Exact large-scale correlations in diffusive systems with general interactions: explicit characterisation without the Dean--Kawasaki equation
• Macroscopic fluctuation theory of interacting Brownian particles
• Structure of the optimal path to a fluctuation