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Multibaker map for thermodynamic cross effects in 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 presents a deterministic model for heat and particle transport, including cross effects and entropy balance. The model, using a multibaker map, accurately describes thermodynamic transport equations and uniform temperature distributions.

Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Dynamical Systems

Background:

  • Simultaneous heat and particle transport, including cross effects, requires a consistent theoretical framework.
  • Entropy balance is crucial for understanding irreversible processes in thermodynamic systems.
  • Deterministic dynamical systems offer a rigorous approach to modeling complex physical phenomena.

Purpose of the Study:

  • To provide a consistent description of simultaneous heat and particle transport within a deterministic dynamical system.
  • To incorporate cross effects and ensure thermodynamic entropy balance.
  • To develop a model that can mimic spatial temperature distributions and their evolution.

Main Methods:

  • Utilizing a multibaker map framework.

Related Experiment Videos

  • Introducing a second field with source terms to represent spatial temperature distribution.
  • Defining conditions for consistency in the continuum limit with thermodynamic entropy balance.

    • Main Results:

    • The model consistently describes simultaneous heat and particle transport, including cross effects.
    • Conditions were derived for consistency with thermodynamic entropy balance.
    • The model allows for the entropy flux into the surroundings to be a free parameter, leading to different transport properties or uniform temperature distributions.

    Conclusions:

    • The developed multibaker map model provides a unified approach to heat and particle transport.
    • The model's flexibility allows for the investigation of various transport scenarios, from standard thermodynamic transport to thermostated systems.
    • This framework offers insights into nonequilibrium phenomena and their connection to fundamental thermodynamic principles.