Current fluctuations at a phase transition

TL;DR

This paper investigates current fluctuations in the ABC model, a non-equilibrium system with a phase transition, revealing singular behavior and anomalous scaling of cumulants near the transition point.

Contribution

It introduces an effective theory predicting anomalous current fluctuation scaling at the phase transition in the ABC model.

Findings

Cumulants of particle currents become singular near the transition

Current fluctuations exhibit anomalous size dependence at criticality

An effective theory successfully predicts the anomalous scaling behavior

Abstract

The ABC model is a simple diffusive one-dimensional non-equilibrium system which exhibits a phase transition. Here we show that the cumulants of the currents of particles through the system become singular near the phase transition. At the transition, they exhibit an anomalous dependence on the system size (an anomalous Fourier's law). An effective theory for the dynamics of the single mode which becomes unstable at the transition allows one to predict this anomalous scaling.