An experimental test of the Gallavotti-Cohen fluctuation theorem

Ciliberto, S.; Laroche, C.

doi:10.1051/jp4:1998629

Cited by 127 publications

(152 citation statements)

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“…Our theory of finite time corrections for the analysis of our numerical data could in principle be of interest for real experimental settings where non Gaussian fluctuations for the entropy production rate are observed, see [35,36].…”

Section: Discussionmentioning

confidence: 99%

Fluctuation Relation beyond Linear Response Theory

2005

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The Fluctuation Relation (FR) is an asymptotic result on the distribution of certain observables averaged over time intervals τ as τ → ∞ and it is a generalization of the fluctuation-dissipation theorem to far from equilibrium systems in a steady state which reduces to the usual Green-Kubo (GK) relation in the limit of small external non conservative forces. FR is a theorem for smooth uniformly hyperbolic systems, and it is assumed to be true in all dissipative "chaotic enough" systems in a steady state. In this paper we develop a theory of finite time corrections to FR, needed to compare the asymptotic prediction of FR with numerical observations, which necessarily involve fluctuations of observables averaged over finite time intervals τ . We perform a numerical test of FR in two cases in which non Gaussian fluctuations are observable while GK does not apply and we get a non trivial verification of FR that is independent of and different from linear response theory. Our results are compatible with the theory of finite time corrections to FR, while FR would be observably violated, well within the precision of our experiments, if such corrections were neglected.

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Section: Discussionmentioning

confidence: 99%

Fluctuation Relation beyond Linear Response Theory

2005

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“…This has been performed with local temperature fluctuations in RayleighBénard convection [30]. Although more than vaguely related to the injected power or to the entropy creation rate, it has been shown that the local temperature fluctuations follow a law of the form (9).…”

Section: Experimental Checks Of the Fluctuation Theoremmentioning

confidence: 99%

“…Without averaging on time, we have also checked that log Π(P ) Π(−P ) is linear in P . One might then think that β(τ ) could be represented over the entire range of τ as β(τ ) = β(τ = ∞) + constant/τ , as observed for temperature fluctuations in [30]; this is not true in our case: although β(τ ) is linear in 1/τ for large 1/τ , its difference from its asymptotic value β goes to zero much faster than 1/τ for small 1/τ .…”

Section: "Test Of the Fluctuation Theorem"mentioning

confidence: 99%

Power injected in dissipative systems and the fluctuation theorem

Aumaître¹,

Fauve²,

et al. 2001

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Abstract.We consider three examples of dissipative dynamical systems involving many degrees of freedom, driven far from equilibrium by a constant or time dependent forcing. We study the statistical properties of the injected and dissipated power as well as the fluctuations of the total energy of these systems. The three systems under consideration are: a shell model of turbulence, a gas of hard spheres colliding inelastically and excited by a vibrating piston, and a Burridge-Knopoff spring-block model. Although they involve different types of forcing and dissipation, we show that the statistics of the injected power obey the "fluctuation theorem" demonstrated in the case of time reversible dissipative systems maintained at constant total energy, or in the case of some stochastic processes. Although this may be only a consequence of the theory of large deviations, this allows a possible definition of "temperature" for a dissipative system out of equilibrium. We consider how this "temperature" scales with the energy and the number of degrees of freedom in the different systems under consideration. PACS

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“…The large deviation function G L,ℓ (J; ρ a , ρ b ), defined as in (1.1), depends of course on the size ℓ of the slit. One reason for considering the fluctuations of this partial current is that in experiments it is often only possible to measure the fluctuations of local quantities and not of global quantities [10,9].…”

Section: Introductionmentioning

confidence: 99%

Vortices in the Two-Dimensional Simple Exclusion Process

Bodineau

Derrida²,

Lebowitz

2008

J Stat Phys

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Abstract. We show that the fluctuations of the partial current in two dimensional diffusive systems are dominated by vortices leading to a different scaling from the one predicted by the hydrodynamic large deviation theory. This is supported by exact computations of the variance of partial current fluctuations for the symmetric simple exclusion process on general graphs. On a two-dimensional torus, our exact expressions are compared to the results of numerical simulations. They confirm the logarithmic dependence on the system size of the fluctuations of the partial flux. The impact of the vortices on the validity of the fluctuation relation for partial currents is also discussed in an Appendix.

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An experimental test of the Gallavotti-Cohen fluctuation theorem

Cited by 127 publications

References 1 publication

Fluctuation Relation beyond Linear Response Theory

Fluctuation Relation beyond Linear Response Theory

Power injected in dissipative systems and the fluctuation theorem

Vortices in the Two-Dimensional Simple Exclusion Process

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