Modelling thermostatting, entropy currents and cross effects by dynamical systems

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 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.

15 pages (revtex), 6 figures (eps)

References in corpus (4)

• Gibbs entropy and irreversible thermodynamics
• Thermostating by Deterministic Scattering: Heat and Shear Flow
• A MultiBaker Map for Thermodynamic Cross-Effects in Dynamical Systems
• Thermodynamic Cross-Effects from Dynamical Systems

Cited by in corpus (8)

• Increasing thermoelectric efficiency towards the Carnot limit
• Thermoelectric efficiency in momentum-conserving systems
• Diffusive Lorentz gases and multibaker maps are compatible with irreversible thermodynamics
• Quantum Multibaker Maps: Extreme Quantum Regime
• Shear flow, viscous heating, and entropy balance from dynamical systems
• A multibaker map for shear flow and viscous heating
• 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