Modeling thermostating, entropy currents, and cross effects by dynamical systems

A generalized multibaker map with periodic boundary conditions is shown to model boundary-driven transport, when the driving is applied by a "perturba tion" of the dynamics localized in a macroscopically small region.]In this case there are sustained density gradients in the steady state. A non-unifo rm stationary temperature profile can be maintained by incorporating a heat source into the dynamics, which deviates from the one of a bulk system onl y in a (macroscopically small) localized region such that a heat (or entrop y) flux can enter an attached thermostat only in that region. For these set tings the relation between the average phase-space contraction, the entropy flux to the thermostat and irreversible entropy production is clarified fo r stationary and non-stationary states. In addition, thermoelectric cross e ffects are described by a multibaker chain consisting of two parts with dif ferent transport properties, modeling a junction between two metals.