Anomalous System Size Dependence of Large Deviation Functions for Local Empirical Measure

TL;DR

This paper investigates the unusual dependence of large deviation functions on system size for local empirical measures in low-dimensional diffusive systems without macroscopic flow, revealing an anomaly linked to long-time tail effects.

Contribution

It uncovers an anomalous system size dependence of large deviation functions in low-dimensional diffusive systems and analyzes its relation to long-time tail phenomena.

Findings

Large deviation functions depend anomalously on system size in 1D and 2D systems.

The anomaly is linked to the absence of macroscopic flow.

Long-time tail behavior is related to the observed anomaly.

Abstract

We study the large deviation function for the empirical measure of diffusing particles at one fixed position. We find that the large deviation function exhibits anomalous system size dependence in systems that satisfy the following conditions: (i) there exists no macroscopic flow, and (ii) their space dimension is one or two. We investigate this anomaly by using a contraction principle. We also analyze the relation between this anomaly and the so-called long-time tail behavior on the basis of phenomenological arguments.