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Exact free energy functional for a driven diffusive open stationary nonequilibrium system.

B Derrida1, J L Lebowitz, E R Speer

  • 1Laboratoire de Physique Statistique, 24 rue Lhomond, 75231 Paris Cedex 05, France. derrida@lps.ens.fr

Physical Review Letters
|July 30, 2002
PubMed
Summary

Researchers derived the exact probability for macroscopic density profiles in open driven diffusive systems. This reveals a novel nonequilibrium free energy with unique properties reflecting system dynamics and phase transitions.

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Area of Science:

  • Statistical Physics
  • Non-equilibrium Thermodynamics
  • Condensed Matter Physics

Background:

  • Understanding the steady states of open driven diffusive systems is crucial for many areas of physics and chemistry.
  • Previous models often simplified system dynamics, limiting their applicability to complex phenomena like phase transitions.

Purpose of the Study:

  • To derive the exact probability of macroscopic density profiles in the stationary nonequilibrium state of open driven diffusive systems.
  • To characterize the properties of the nonequilibrium free energy (F) and its relation to system dynamics.

Main Methods:

  • The study employs analytical methods to derive the probability in the thermodynamic limit (system size L → ∞).
  • Focuses on the structure and properties of the nonequilibrium free energy function F.

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  • Analyzes the implications of system dynamics, such as shocks and phase transitions, on F.

    • Main Results:

    • The exact probability is found to be exp[-LF([rho(x)])], where L is system size.
    • The nonequilibrium free energy (F) exhibits a nonlocal structure, distinct from purely diffusive systems.
    • Nonconvexity of F, discontinuities in its second derivatives, and non-Gaussian fluctuations are observed, reflecting system shocks and dynamic phase transitions.

    Conclusions:

    • The derived nonequilibrium free energy (F) provides a new framework for understanding stationary states in driven diffusive systems.
    • The study highlights the connection between dynamic phase transitions and the mathematical properties of F.
    • Findings offer insights into non-Gaussian fluctuations and emergent behaviors in open, driven systems.