A MASTER EQUATION APPROACH TO FLUCTUATING HYDRODYNAMICS - HEAT-CONDUCTION

It is show that a recently proposed stochastic formulation of fluid dynamics makes possible a new approach to heat conduction and to temperature fluctuations. A master equation is presented which describes the time evolution of the probability distribution of a multivariate stochastic temperature variable. Splitting the stochastic variable in a macroscopic and a small fluctuating part and performing an expansion in powers of the inverse number of degrees of freedom per volume element of fluid the corresponding equations of fluctuating hydrodynamics are recovered. Stochastic simulations based on the generation of realizations of the stochastic process demonstrate the computational power of the approach.