  A consistent description of simultaneous heat and particle transport,
including cross effects, and the associated entropy balance is given in the
framework of a deterministic dynamical system. This is achieved by a multibaker
map where, besides the phase-space density of the multibaker, a second field
with appropriate source terms is included in order to mimic a spatial
temperature distribution and its time evolution. Conditions are given to ensure
consistency in an appropriately defined continuum limit with the thermodynamic
entropy balance. They leave as the only free parameter of the model the entropy
flux let directly into a surroundings. If it vanishes in the bulk, the
transport properties of the model are described by the thermodynamic transport
equations. Another choice leads to a uniform temperature distribution. It
represents transport problems treated by means of a thermostatting algorithm,
similar to the one considered in non-equilibrium molecular dynamics.
