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

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 with translational symmetry if and only if they satisfy the following conditions: (i) there exists no macroscopic flow, and (ii) their space dimension is one or two. We analyze the relation between this anomaly and the so-called long-time tail behavior on the basis of phenomenological arguments. We also investigate this anomaly by using a contraction principle.