Fluctuation Theorem for heat flow between thermal reservoirs

Abstract

We consider thermal conduction in a classical many body system which is in contact with two isothermal reservoirs maintained at different temperatures. We calculate from first principles, the probability that when observed for a finite time, the time averaged heat flux flows in the reverse direction to that required by the Second Law of Thermodynamics. Analytical expressions are given for the probability of observing Second Law violating dynamical fluctuations in this system. These expressions constitute an application of the Fluctuation Theorem to the problem of thermal conduction. We prove that the probability of observing fluctuations in the heat flux which violate the Second Law is related to time averaged fluctuations in the irreversible entropy production. Our expressions are tested using nonequilibrium molecular dynamics simulations of heat flow between thermostatted walls.