Fluctuation theorem for constrained equilibrium systems

Details Fluctuation theorem for constrained equilibrium systems Fluctuation theorem for constrained equilibrium systems

2006-01-19

arxiv.org/abs/cond-mat/0601435v1

Phys. Rev. E 73, 026121 (2006) [5 pages]

Physics

Condensed Matter

Statistical Mechanics

To appear in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.73.026121

We discuss the fluctuation properties of equilibrium chaotic systems with constraints such as iso-kinetic and Nos\'e-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 non-trivial fluctuations which we show satisfy a simple version of the Gallavotti-Cohen fluctuation theorem, complementary to the usual fluctuation theorem for non-equilibrium stationary states, and appropriate to constrained equilibrium states. Moreover we show 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 Nos\'e-Hoover thermostatting; (iii) a simple hyperbolic two-dimensional map.

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