Validity of the additivity principle in the weakly asymmetric exclusion process with open boundaries

TL;DR

This paper tests the additivity principle in the weakly asymmetric exclusion process with open boundaries using numerical methods, confirming its validity for current fluctuations and density profiles without evidence of phase transitions.

Contribution

It provides numerical validation of the additivity principle in a specific stochastic process, extending its applicability to open boundary conditions.

Findings

Convergence of cumulant generating function to theoretical predictions

Agreement of density profiles with additivity principle

No evidence of dynamical phase transitions

Abstract

The additivity principle allows a calculation of current fluctuations and associated density profiles in large diffusive systems. In order to test its validity in the weakly asymmetric exclusion process with open boundaries, we use a numerical approach based on the density matrix renormalisation. With this technique, we determine the cumulant generating function of the current and the density profile corresponding to atypical currents in finite systems. We find that these converge to those predicted by the additivity principle. No evidence for dynamical phase transitions is found.