A Local Fluctuation Theorem

The Fluctuation Theorem (FT) gives an analytic expression for the probability, in a nonequilibrium system of finite size observed for a finite time, that the dissipative flux will flow in the reverse direction to that required by the Second Law of Thermodynamics. In the present letter a Local version of the Fluctuation Theorem (LFT), is derived. We find that in the case of planar Poiseuille flow of a Newtonian fluid between thermostatted walls, non-equilibrium molecular dynamics simulation results support LFT.