Thermodynamic cross effects from dynamical systems

We give a thermodynamically consistent description of simultaneous heat and particle transport, as well as of the associated cross effects, in the fra mework of a chaotic dynamical system, a generalized multibaker map. Besides the density, a second field with appropriate source terms is included in o rder to mimic, after coarse graining, a spatial temperature distribution an d its time evolution. An expression is derived for the irreversible entropy production in a steady state, as the average of the growth rate of the rel ative density, a unique combination of the two fields.