The fluctuation-dissipation theorem

Kubo, Ryogo

doi:10.1088/0034-4885/29/1/306

Cited by 4,634 publications

(3,654 citation statements)

References 25 publications

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“…The motion of a diffusing particle of mass m evolving in a stationary medium is usually described by the generalized Langevin equation [4], [5],…”

Section: Diffusion In a Stationary Mediummentioning

confidence: 99%

“…When the environment is a thermal bath, the noise spectral density and the real part of the friction coefficient are related by the fluctuation-dissipation theorem of the second kind [4], [5]. Thermalizing particle variables such as the particle velocity then satisfy the fluctuation-dissipation theorem of the first kind i.e.…”

Section: Introductionmentioning

confidence: 99%

“…Thermalizing particle variables such as the particle velocity then satisfy the fluctuation-dissipation theorem of the first kind i.e. the Einstein relation [4], [5].…”

Section: Introductionmentioning

confidence: 99%

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Anomalous diffusion of a particle in an aging medium

Pottier

Mauger

2004

Physica A: Statistical Mechanics and its Applications

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We report new results about the anomalous diffusion of a particle in an aging medium. For each given age, the quasi-stationary particle velocity is governed by a generalized Langevin equation with a frequency-dependent friction coefficient proportional to |ω| δ−1 at small frequencies, with 0 < δ < 2. The aging properties of the medium are encoded in a frequency dependent effective temperature T eff. (ω). The latter is modelized by a function proportional to |ω| α at small frequencies, with α < 0, thus allowing for the medium to have a density of slow modes proportionally larger than in a thermal bath. Using asymptotic Fourier analysis, we obtain the behaviour at large times of the velocity correlation function and of the mean square displacement. As a result, the anomalous diffusion exponent in the aging medium appears to be linked, not only to δ as it would be the case in a thermal bath, but also to the exponent α characterizing the density of slow modes.

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“…The motion of a diffusing particle of mass m evolving in a stationary medium is usually described by the generalized Langevin equation [4], [5],…”

Section: Diffusion In a Stationary Mediummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Anomalous diffusion of a particle in an aging medium

Pottier

Mauger

2004

Physica A: Statistical Mechanics and its Applications

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“…In spite of their apparent random origin, essential physical information is encoded therein [1]. A classical example is the fluctuation-dissipation theorem, which relates the linear response of a system to an external perturbation to the fluctuation properties of the system in thermal equilibrium [2,3]. More recently, the investigation of general properties of fluctuations in nonequilibrium steady states is opening new paths for understanding physics far from equilibrium [4][5][6][7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Renormalized time scale for anticipating and lagging synchronization

2016

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We consider fluctuations of the dissipated energy in nonlinear driven diffusive systems subject to bulk dissipation and boundary driving. With this aim, we extend the recently-introduced macroscopic fluctuation theory to nonlinear driven dissipative media, starting from the fluctuating hydrodynamic equations describing the system mesoscopic evolution. Interestingly, the action associated to a path in mesoscopic phase-space, from which large-deviation functions for macroscopic observables can be derived, has the same simple form as in non-dissipative systems. This is a consequence of the quasi-elasticity of microscopic dynamics, required in order to have a nontrivial competition between diffusion and dissipation at the mesoscale. Euler-Lagrange equations for the optimal density and current fields that sustain an arbitrary dissipation fluctuation are also derived. A perturbative solution thereof shows that the probability distribution of small fluctuations is always gaussian, as expected from the central limit theorem. On the other hand, strong separation from the gaussian behavior is observed for large fluctuations, with a distribution which shows no negative branch, thus violating the Gallavotti-Cohen fluctuation theorem as expected from the irreversibility of the dynamics. The dissipation large-deviation function exhibits simple and general scaling forms for weakly and strongly dissipative systems, with large fluctuations favored in the former case but heavily supressed in the latter. We apply our results to a general class of diffusive lattice models for which dissipation, nonlinear diffusion and driving are the key ingredients. The theoretical predictions are compared to extensive numerical simulations of the microscopic models, and excellent agreement is found. Interestingly, the large-deviation function is in some cases non-convex beyond some dissipation. These results show that a suitable generalization of macroscopic fluctuation theory is capable of describing in detail the fluctuating behavior of nonlinear driven dissipative media.

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“…This calls to mind the fluctuation-dissipation theorem (e.g., KUBO, 1966) which states a relation between the Green function between two points and the correlation of the random fluctuations of the field at these two points. Originally, this relation was developed for thermal noise.…”

Section: Field Correlation In the Seismic Noisementioning

confidence: 99%

Phase and Correlation in ‘Random’ Seismic Fields and the Reconstruction of the Green Function

Campillo¹,

Derode²,

Larose³

et al.

Pageoph Topical Volumes

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Abstract-We first present a summary of recent results on coda interpretation. We emphasize the observation of the stabilization of P to S energy ratio indicating the modal equipartition of the wavefield. This property clearly shows that the coda waves are in the regime of multiple scattering. Numerical solutions of the elastic radiative transfer equation are used to illustrate the evolution of the wave-field towards P-to-S energy stabilization, and asymptotically to complete isotropy. The energy properties of the coda have been widely studied but the phase properties have often been neglected. The recently observed coherent backscattering enhancement, an expression of the so-called 'weak localization', demonstrates that interference effects still persist for multiple diffracted waves. Another manifestation of the persistence of the phase is the possibility to reconstruct the Green function between two stations by averaging the cross correlation of coda waves produced by distant earthquakes and recorded at those two stations. This reconstruction is directly related to the properties of reciprocity and time reversal of any wavefield. Using broadband seismic coda waves, we show that the dominant phases of the Green function in the band 2 s-10 s, namely fundamental mode Rayleigh and Love waves, are reconstructed. We analyze the time symmetry of the cross correlation and show how the level of symmetry evolves with the isotropization of the diffuse field with lapse time. Similarly we investigate the correlation in continuous ambient noise records. Whereas the randomness of the coda results from multiple scattering by randomly distributed scatterers, we assume that the seismic noise is random mostly because of the distribution of sources at the surface of the Earth. Surface waves can be extracted from long time series. The dispersion curves of Rayleigh waves are deduced from the correlations. On paths where measurements from earthquake data are also available, we show that they are in good agreement with those deduced from noise correlation. The measurement of velocities from correlation of noise along paths crossing different crustal structures opens the way for a 'passive imaging' of the Earth's structure.

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The fluctuation-dissipation theorem

Abstract: Contents 1. Introduction . 2. Einstein relation . 3. Classical Langevin equation and the random force I 4. Generalized Langevin equation .

Cited by 4,634 publications

References 25 publications

Anomalous diffusion of a particle in an aging medium

Anomalous diffusion of a particle in an aging medium

Renormalized time scale for anticipating and lagging synchronization

Phase and Correlation in ‘Random’ Seismic Fields and the Reconstruction of the Green Function

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