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Detailed fluctuation theorem for mesoscopic modeling.

E A J F Peters1

  • 1Department of Chemical Engineering, Technische Universiteit Eindhoven, Den Dolech 2, Postbus 513, 5600 MB Eindhoven, The Netherlands. e.a.j.f.peters@tue.nl

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 9, 2005
PubMed
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A detailed fluctuation theorem is derived using microscopic time reversibility and phase space incompressibility. This theorem connects forward and time-reversed processes, offering insights into non-equilibrium thermodynamics and mesoscopic equations.

Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Non-equilibrium Systems

Background:

  • Microscopic reversibility and phase space incompressibility (Liouville's theorem) are fundamental.
  • Understanding non-equilibrium systems requires robust theoretical frameworks.

Purpose of the Study:

  • To derive a detailed fluctuation theorem.
  • To explore its implications for mesoscopic descriptions and simulation techniques.

Main Methods:

  • Derivation based on phase space incompressibility and time reversibility.
  • Analysis of conditional probabilities for forward and time-reversed processes.
  • Investigation of constraints on mesoscopic equations.

Main Results:

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  • The fluctuation theorem relates forward and time-reversed conditional probabilities.
  • The ratio of probabilities is linked to entropy differences.
  • The theorem holds under local equilibrium conditions, even far from equilibrium.
  • Constraints are imposed on mesoscopic equations, including a generalized kinetic form for stochastic differential equations.

    • Conclusions:

    • The derived fluctuation theorem provides a powerful tool for non-equilibrium statistical mechanics.
    • It enables the development of thermodynamically consistent simulation methods.
    • The theorem offers insights into the structure of mesoscopic dynamics and its connection to microscopic laws.