Fluctuation theorem for constrained equilibrium systems

Thomas Gilbert and J. Robert Dorfman
Phys. Rev. E 73, 026121 – Published 17 February 2006

Abstract

We discuss the fluctuation properties of equilibrium chaotic systems with constraints such as isokinetic and Nosé-Hoover thermostats. Although the dynamics of these systems does not typically preserve phase-space volumes, the average phase-space contraction rate vanishes, so that the stationary states are smooth. Nevertheless, finite-time averages of the phase-space contraction rate have nontrivial fluctuations which we show satisfy a simple version of the Gallavotti-Cohen fluctuation theorem, complementary to the usual fluctuation theorem for nonequilibrium stationary states and appropriate to constrained equilibrium states. Moreover, we show that these fluctuations are distributed according to a Gaussian curve for long enough times. Three different systems are considered here: namely, (i) a fluid composed of particles interacting with Lennard-Jones potentials, (ii) a harmonic oscillator with Nosé-Hoover thermostatting, and (iii) a simple hyperbolic two-dimensional map.

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  • Received 19 October 2005

DOI:https://doi.org/10.1103/PhysRevE.73.026121

©2006 American Physical Society

Authors & Affiliations

Thomas Gilbert1,* and J. Robert Dorfman2,†

  • 1Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium
  • 2Department of Physics and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA

  • *Electronic address: thomas.gilbert@ulb.ac.be
  • Electronic address: rdorfman@umd.edu

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Vol. 73, Iss. 2 — February 2006

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