Weak additivity principle for current statistics in d-dimensions

TL;DR

This paper extends the additivity principle to higher-dimensional driven diffusive systems, demonstrating that a weak version of the principle provides better predictions for current fluctuations than straightforward extensions.

Contribution

It introduces and validates a weak additivity principle for d-dimensional systems, improving the understanding of current statistics beyond one dimension.

Findings

Weak AP outperforms straightforward extension in predicting current fluctuations.

Numerical simulations and microscopic calculations support the weak AP.

Structured current vector fields are crucial in higher 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.