Infinite family of universal profiles for heat current statistics in Fourier's law

TL;DR

This paper uses large deviation theory to analyze heat current fluctuations in a driven fluid, revealing universal temperature profiles, logarithmic tails for large deviations, and explicit cumulant relations.

Contribution

It introduces an infinite family of universal profiles for heat current statistics, providing a comprehensive classification and analysis of atypical current fluctuations.

Findings

Universal temperature profiles for atypical currents

Logarithmic tails in large current fluctuations

Explicit relations between cumulants of the current distribution

Abstract

Using tools from large deviation theory, we study fluctuations of the heat current in a model of $d$-dimensional incompressible fluid driven out of equilibrium by a temperature gradient. We find that the most probable temperature fields sustaining atypical values of the global current can be naturally classified in an infinite set of curves, allowing us to exhaustively analyze their topological properties and to define universal profiles onto which all optimal fields collapse. We also compute the statistics of empirical heat current, where we find remarkable logarithmic tails for large current fluctuations orthogonal to the thermal gradient. Finally, we determine explicitly a number of cumulants of the current distribution, finding remarkable relations between them.