Abstract
Abstract A stochastic approach to the energy balance equation of nonequilibrium thermodynamics is suggested. The stochastic formulation interprets the temperature field as a multivariate stochastic process which is governed by a master equation. By means of a systematic expansion in powers 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. The master equation formulation gives rise to a new stochastic simulation method which is illustrated by applying it to heat conduction and temperature fluctuations in a fluid between two infinite parallel planes which are kept at different temperatures.
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