Fluctuation relations in simple examples of non-equilibrium steady states

Chétrite, Raphaël; Falkovich, Gregory; Gawędzki, Krzysztof

doi:10.1088/1742-5468/2008/08/p08005

Cited by 105 publications

(198 citation statements)

References 47 publications

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“…For 2D flows, a linear friction is introduced through the −αu term (α = 0 in 3D), to prevent the accumulation of energy at scales larger than l D = α −3=2 « 1=2 . The Lagrangian information is then obtained by integrating in time the equation of motion of fluid tracers dX dt = VðtÞ = uðX,tÞ, [5] in which the tracer velocity VðtÞ is the same as the fluid velocity u at position X and time t.…”

Section: Methodsmentioning

confidence: 99%

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Flight–crash events in turbulence

Pumir

Falkovich

et al. 2014

Proc. Natl. Acad. Sci. U.S.A.

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108

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The statistical properties of turbulence differ in an essential way from those of systems in or near thermal equilibrium because of the flux of energy between vastly different scales at which energy is supplied and at which it is dissipated. We elucidate this difference by studying experimentally and numerically the fluctuations of the energy of a small fluid particle moving in a turbulent fluid. We demonstrate how the fundamental property of detailed balance is broken, so that the probabilities of forward and backward transitions are not equal for turbulence. In physical terms, we found that in a large set of flow configurations, fluid elements decelerate faster than accelerate, a feature known all too well from driving in dense traffic. The statistical signature of rare "flight-crash" events, associated with fast particle deceleration, provides a way to quantify irreversibility in a turbulent flow. Namely, we find that the third moment of the power fluctuations along a trajectory, nondimensionalized by the energy flux, displays a remarkable power law as a function of the Reynolds number, both in two and in three spatial dimensions. This establishes a relation between the irreversibility of the system and the range of active scales. We speculate that the breakdown of the detailed balance characterized here is a general feature of other systems very far from equilibrium, displaying a wide range of spatial scales. I n systems at thermal equilibrium, the probabilities of forward and backward transitions between any two states are equal, a property known as "detailed balance." This fundamental property expresses time reversibility of equilibrium statistics (1). In the important class of nonequilibrium problems, where the dynamics of the system is coupled with a heat bath, the notion of detailed balance can be extended and fluctuation theorems successfully describe the behavior (2, 3). This class contains many experimental situations (4) where quantitative information on irreversibility was obtained (3). When a system driven by thermal noise is characterized by a probability current, the fluctuationdissipation theorem and detailed balance was found to apply in a comoving reference frame (5).In comparison, very little is known concerning the statistical properties of a small part embedded in a fluctuating, turbulent background. The fundamental notion of detailed balance is not expected to apply in such systems. Here we ask, what does the time irreversibility inherent to the large system imply for the statistical properties of small parts in the system and how do we measure the degree of irreversibility (6, 7) (or equivalently, how far is the system away from equilibrium) by monitoring a small part in the system? We focus here on fluid turbulence, a paradigm for ultimate far-from-equilibrium states, where irreversibility of fluctuations is a fundamental property (8, 9). We show that the simplest and most fundamental scalar quantity, namely, the kinetic energy of a fluid particle, enables a clear identification and qua...

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Section: Methodsmentioning

confidence: 99%

“…This class contains many experimental situations (4) where quantitative information on irreversibility was obtained (3). When a system driven by thermal noise is characterized by a probability current, the fluctuationdissipation theorem and detailed balance was found to apply in a comoving reference frame (5).…”

mentioning

confidence: 99%

Flight–crash events in turbulence

Pumir

Falkovich

et al. 2014

Proc. Natl. Acad. Sci. U.S.A.

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108

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“…Note that the term on the right hand side of (12.3) violating the standard fluctuation-dissipation theorem (11.6) contains the constant flux of the probability current j(x) as a factor. Proof of Proposition 6 and of its version with A a replaced by O a will be given in [12].…”

Section: One-dimensional Langevin Equation With Flux Solutionmentioning

confidence: 99%

Fluctuation Relations for Diffusion Processes

Chétrite

Gawędzki

2008

Commun. Math. Phys.

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154

349

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The paper presents a unified approach to different fluctuation relations for classical nonequilibrium dynamics described by diffusion processes. Such relations compare the statistics of fluctuations of the entropy production or work in the original process to the similar statistics in the time-reversed process. The origin of a variety of fluctuation relations is traced to the use of different time reversals. It is also shown how the application of the presented approach to the tangent process describing the joint evolution of infinitesimally close trajectories of the original process leads to a multiplicative extension of the fluctuation relations.

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“…Such an additive structure was found previously [28,32] without, however, giving the correction term a transparent physical meaning. In the special case of a driven Langevin particle [23], the correction term has been identified as a correlation function involving the local mean velocity and has later been rationalized by observing the process in the locally comoving frame [33,34]. Generally, the observable occurring in the first term in Eq.…”

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confidence: 99%

Fluctuation-dissipation theorem in nonequilibrium steady states

2010

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Abstract. -In equilibrium, the fluctuation-dissipation theorem (FDT) expresses the response of an observable to a small perturbation by a correlation function of this variable with another one that is conjugate to the perturbation with respect to energy. For a nonequilibrium steady state (NESS), the corresponding FDT is shown to involve in the correlation function a variable that is conjugate with respect to entropy. By splitting up entropy production into one of the system and one of the medium, it is shown that for systems with a genuine equilibrium state the FDT of the NESS differs from its equilibrium form by an additive term involving total entropy production. A related variant of the FDT not requiring explicit knowledge of the stationary state is particularly useful for coupled Langevin systems. The a priori surprising freedom apparently involved in different forms of the FDT in a NESS is clarified.

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Fluctuation relations in simple examples of non-equilibrium steady states

Cited by 105 publications

References 47 publications

Flight–crash events in turbulence

Flight–crash events in turbulence

Fluctuation Relations for Diffusion Processes

Fluctuation-dissipation theorem in nonequilibrium steady states

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