M.Sc Thesis
M.Sc Student Guy Bunin Fluctuation-Dissipation Relations in Driven-Dissipative Systems Department of Physics Full Professor Levine Dov

Abstract

This Thesis investigates the validity of time dependent fluctuation-dissipation (FD) relations, in steady state driven-dissipative systems. The time-dependent FD relation is known to hold in equilibrium systems. This property does not generally extend to non-equilibrium systems. Indeed, we have calculated the FD relation for various models, and have shown that it is generally violated in non-equilibrium steady states. Two classes of models are considered in this work. One is the minimal-dissipative model and its variants, where every particle is represented by a single degree of freedom. The FD relations in steady state are calculated analytically for one-particle and N-particle measurements. The FD relation holds for the one-particle measurement, but is violated for the N-particle measurement. In a variant of the model, the one-particle FD relation is also violated. The second class of models are the hard-sphere models. In the simplest variant, the Maxwell model, time-dependent FD relations are shown to hold. Moreover, the FD temperature is shown to coincide with the average energy of the system, known as the granular temperature.  In a more realistic model the FD relation is shown to be violated. The results indicate, however, that the violation is small, i.e. the variation of the FD temperature is in the order of a few percent .