A MultiBaker Map for Thermodynamic Cross-Effects in Dynamical Systems

Abstract

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.

18 pages, 3 postscript figures

References in corpus (3)

• Thermostating by Deterministic Scattering: Heat and Shear Flow
• Thermodynamic Cross-Effects from Dynamical Systems
• Critical states of transient chaos

Cited by in corpus (9)

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• Escape-rate formalism, decay to steady states, and divergences in the entropy-production rate
• Reply to E.G.D. Cohen, L. Rondoni, Physica A 306 (2002) 117
• A law of order estimation and leading-order terms for a family of averaged quantities on a multibaker chain system