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We set up a discrete space-time dynamical model of molecules with thermalisedkinetic energy and repulsive cores, in an external potential. The state isspecified by a probability on the sample space. One time-step is given by abistochastic map, followed by a local thermalising map. The model obeys thefirst and second laws of thermodynamics. The continuum limit, obtained using aMAPLE program, gives rise to coupled nonlinear reaction-diffusion equations forthe density and temperature fields. The system obeys Onsager symmetry andexhibits the Soret and Dufour effects.

The Soret and Dufour effects in statistical dynamics