Fluctuations of the dissipated energy in a granular system

Abstract

Large fluctuations, play an important role in many fields of science as they crucially determine the fate of a system. The statistics of these fluctuations encodes essential information on the physics of the system at hand. This is particularly important in systems far from equilibrium, where no general theory exists up to date capable of predicting macroscopic and fluctuating behavior in terms of microscopic physics.The study of fluctuations far from equilibrium may open the door to such general theory. In this work we follow this path by studying the fluctuations of the dissipated energy in an oversimplified model of a granular system. The model, first proposed and solved by Levanony and Levine [1], is a simple one dimensional diffusive lattice system which includes energy dissipation as a main ingredient. When subject to boundary heat baths, the system reaches an steady state characterized by a highly nonlinear temperature profile and a nonzero average energy dissipation. For long but finite times, the time‐averaged dissipated energy fluctuates, obeying a large deviation principle. We study the large deviation function (LDF) of the dissipated energy by means of advanced Monte Carlo techniques [2], arriving to the following results: (i) the LDF of the dissipated energy has only a positive branch, meaning that for long times only positive dissipation is expected, (ii) as a result of microscopic time‐irreversibility, the LDF does not obeys the Gallavotti‐Cohen fluctuation theorem, (iii) the LDF is Gaussian around the average dissipation, but non‐Gaussian, asymmetric tails quickly develop away from the average, and (iv) the granular system adopts a precise optimal profile in order to facilitate a given dissipation fluctuation, different from the steady profile. We compare our numerical results with predictions based on hydrodynamic fluctuation theory [3], finding good agreement.