Abstract
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 localized 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, modeling a junction between two metals.
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Vollmer, J., Tél, T. & Mátyás, L. Modeling Thermostating, Entropy Currents, and Cross Effects by Dynamical Systems. Journal of Statistical Physics 101, 79–105 (2000). https://doi.org/10.1023/A:1026499113431
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DOI: https://doi.org/10.1023/A:1026499113431