Multibaker map for thermodynamic cross effects in dynamical systems

A consistent description of simultaneous heat and particle transport, inclu ding cross effects, and the associated entropy balance is given in the fram ework of a deterministic dynamical system. This is achieved by a multibaker map where, in addition to the phase-space density of the multibaker, a sec ond field with appropriate source terms is included in order to mimic a spa tial 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 the surroundings. If it vanishes in the bulk, the transport properties of the model are described by the the rmodynamic transport equations. Another choice leads to a uniform temperatu re distribution. It represents transport problems treated by means of a the rmostating algorithm, similar to the one considered in nonequilibrium molec ular dynamics.