  A generalized multibaker map with periodic boundary conditions is shown to
model boundary-driven transport, when the driving is applied by a
``perturbation'' of the dynamics localised in a macroscopically small region.
In this case there are sustained density gradients in the steady state. A
non-uniform stationary temperature profile can be maintained by incorporating a
heat source into the dynamics, which deviates from the one of a bulk system
only in a (macroscopically small) localized region such that a heat (or
entropy) flux can enter an attached thermostat only in that region. For these
settings the relation between the average phase-space contraction, the entropy
flux to the thermostat and irreversible entropy production is clarified for
stationary and non-stationary states. In addition, thermoelectric cross-effects
are described by a multibaker chain consisting of two parts with different
transport properties, modelling a junction between two metals.
