THERMOSTOCHASTICS - HEAT-CONDUCTION AND TEMPERATURE-FLUCTUATIONS

A stochastic approach to the energy balance equation of nonequilibrium thermodynamics is suggested. The stochastic formulation interprets th e temperature field as a multivariate stochastic process which is gove rned by a master equation. By means of a systematic expansion in power s of the inverse number of degrees of freedom per volume element it is shown that the expectation value of the stochastic process obeys the macroscopic Fourier equation. The expansion reveals that in the linear noise approximation the fluctuations superimposed on the macroscopic dynamics are governed by the equations of fluctuating hydrodynamics. T he master equation formulation gives rise to a new stochastic simulati on method which is illustrated by applying it to heat conduction and t emperature fluctuations in a fluid between two infinite parallel plane s which are kept at different temperatures.