Fluctuation theorem for heat flow

Thermal conduction in a classical many-body system which is in contact with tno isothermal reservoirs maintained at different temperatures is consider ed. 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 Seco nd Law of Thermodynamics is calculated from first principles. Analytical ex pressions are given for tile probability of observing Second Law violating fluctuations in this system. These expressions constitute an application of the fluctuation theorem ro the problem of thermal conduction. The expressi ons are tested using nonequilibrium molecular dynamics simulations of heat flow between thermostated walls.