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Fluctuation theorem for constrained equilibrium systems.

Thomas Gilbert1, J Robert Dorfman

  • 1Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium. thomas.gilbert@ulb.ac.be

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 12, 2006
PubMed
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We studied fluctuation properties in constrained equilibrium chaotic systems. Finite-time averages of phase-space contraction rates show Gaussian fluctuations, satisfying a modified Gallavotti-Cohen fluctuation theorem.

Area of Science:

  • Statistical Mechanics
  • Chaos Theory
  • Physical Chemistry

Background:

  • Equilibrium chaotic systems with constraints like isokinetic and Nosé-Hoover thermostats are crucial for understanding complex dynamics.
  • While their dynamics may not preserve phase-space volumes, their stationary states are smooth due to vanishing average phase-space contraction rates.

Purpose of the Study:

  • To investigate the fluctuation properties of phase-space contraction rates in constrained equilibrium chaotic systems.
  • To determine if these fluctuations adhere to a generalized fluctuation theorem and their statistical distribution.

Main Methods:

  • Analysis of finite-time averages of phase-space contraction rates.
  • Application of the Gallavotti-Cohen fluctuation theorem framework.
  • Examination of three distinct systems: Lennard-Jones fluids, harmonic oscillators with Nosé-Hoover thermostats, and 2D hyperbolic maps.

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Main Results:

  • Finite-time averages of phase-space contraction rates exhibit nontrivial fluctuations.
  • These fluctuations satisfy a simplified Gallavotti-Cohen fluctuation theorem, applicable to constrained equilibrium states.
  • The fluctuations are shown to follow a Gaussian distribution for sufficiently long times.

Conclusions:

  • Constrained equilibrium chaotic systems display unique fluctuation properties.
  • The findings extend the applicability of fluctuation theorems to a broader class of systems.
  • The Gaussian nature of these fluctuations provides insights into their statistical behavior.