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