Fluidized Granular Medium as an Instance of the Fluctuation Theorem

Feitosa, Klebert; Menon, Narayanan

doi:10.1103/physrevlett.92.164301

Cited by 157 publications

(248 citation statements)

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“…It is an analog of quantities of recent interest in other nonequilibrium experiments. 8,[14][15][16] The model predicts the backward flows, the bad actors, which are relatively infrequent situations in which particles flow up, rather than down, their concentration gradients. These experiments provide extensive data that go beyond more traditional phenomenological average flux quantities and illuminate the nature of dynamical fluctuations in a simple classical system.…”

Section: Discussionmentioning

confidence: 99%

Measuring Flux Distributions for Diffusion in the Small-Numbers Limit

et al. 2007

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For the classical diffusion of independent particles, Fick's law gives a well-known relationship between the average flux and the average concentration gradient. What has not yet been explored experimentally, however, is the dynamical distribution of diffusion rates in the limit of small particle numbers. Here, we measure the distribution of diffusional fluxes using a microfluidics device filled with a colloidal suspension of a small number of microspheres. Our experiments show that (1) the flux distribution is accurately described by a Gaussian function; (2) Fick's law, that the average flux is proportional to the particle gradient, holds even for particle gradients down to a single particle difference; (3) the variance in the flux is proportional to the sum of the particle numbers; and (4) there are backward flows, where particles flow up a concentration gradient, rather than down it. In addition, in recent years, two key theorems about nonequilibrium systems have been introduced: Evans' fluctuation theorem for the distribution of entropies and Jarzynski's work theorem. Here, we introduce a new fluctuation theorem, for the fluxes, and we find that it is confirmed quantitatively by our experiments.

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Section: Discussionmentioning

confidence: 99%

Measuring Flux Distributions for Diffusion in the Small-Numbers Limit

et al. 2007

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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%

“…32 computed as the ratio ζ (3) /(ζ (2) ) 2 is not measurable within an error of some percent; (ii) usually in a real experiment the accessible time scales are naturally much bigger than the microscopic ones so that, if the negative fluctuations of the entropy production rate are observable at all, one is automatically in the asymptotic regime, where the finite time corrections should be negligible; (iii) a usual problem in a realistic setting is that there is no clear connection between the "natural" thermodynamic entropy production rateṡ = W/T (W is the work of the dissipative external forces and T is the temperature) and the microscopic phase space contraction rate, for which a slope X = 1 in the fluctuation relation ζ(p)− ζ(−p) = Xσ + p is expected; so, often one measures an X = 1 and correspondingly one defines an effective temperature T ef f = T /X giving a natural connection between the effective thermodynamic entropy production rateṡ ef f = W/T ef f and the phase space contraction rate, see [7,35,36]; in such a situation (where an adjustable parameter X appears) it makes no sense to apply our analysis, which is sensible only if one wants to compare the experimental data with a sharp prediction about the slope X in the fluctuation relation.…”

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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“…The fluctuation relation is a parameterless relation and is conjectured to hold in some generality. The discovery of this relation [1] motivated many studies: and experiments specifically designed to its test have been reported on turbulent hydrodynamic flows [2,3,4] and Rayleigh-Bénard convection [5], on liquid crystals [6], on a resistor [7], on granular gases [8].…”

Section: Forewordmentioning

confidence: 99%