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Thermodynamic cross effects from dynamical systems

Matyas1, Tel, Vollmer

  • 1Institute for Theoretical Physics, Eotvos University, P. O. Box 32, H-1518 Budapest, Hungary.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
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This study describes heat and particle transport using a chaotic dynamical system. It derives an expression for irreversible entropy production in a steady state, linking it to density and temperature fields.

Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Dynamical Systems

Background:

  • Understanding simultaneous heat and particle transport is crucial in various physical systems.
  • Cross effects in transport phenomena require sophisticated theoretical frameworks.
  • Chaotic dynamical systems offer a unique perspective for modeling complex transport processes.

Purpose of the Study:

  • To provide a thermodynamically consistent description of simultaneous heat and particle transport.
  • To investigate the associated cross effects within a chaotic dynamical system.
  • To derive an expression for irreversible entropy production in a steady state.

Main Methods:

  • Utilizing a generalized multibaker map as a chaotic dynamical system.
  • Introducing a second field alongside density to model spatial temperature distribution.

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  • Employing coarse-graining techniques to represent macroscopic properties.

    • Main Results:

    • A thermodynamically consistent framework for coupled heat and particle transport is established.
    • The model successfully mimics spatial temperature evolution.
    • An expression for irreversible entropy production in a steady state was derived, based on the relative density growth rate.

    Conclusions:

    • The generalized multibaker map provides a valid model for studying coupled transport phenomena.
    • The derived entropy production expression offers insights into the irreversibility of the system.
    • This approach unifies the description of transport, cross effects, and entropy production.