Fluctuation Theorem for Heat Flow

Thermal conduction in a classical many-body system which is in contact with two isothermal reservoirs maintained at different temperatures is considered. The probability that when observed for a finite time, the heat flux of a finite system flows in the reverse direction to that required by the Second Law of Thermodynamics is calculated from first principles. Analytical expressions are given for the probability of observing Second Law violating fluctuations in this system. These expressions constitute an application of the fluctuation theorem to the problem of thermal conduction. The expressions are tested using non-equilibrium molecular dynamics simulations of heat flow between thermostated walls.