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