Is it possible to experimentally verify the fluctuation relation? A review of theoretical motivations and numerical evidence

Zamponi, Francesco

doi:10.1088/1742-5468/2007/02/p02008

Cited by 27 publications

(32 citation statements)

References 85 publications

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“…Phys. 128, 1337(2007], for the validity of the steady state fluctuation relation, is verified. For the steady state fluctuations of the phase space contraction rate Λ and of the dissipation function Ω, a similar relaxation regime at shorter averaging times is found.…”

Section: Introductionmentioning

confidence: 82%

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On the Fluctuation Relation for Nosé-Hoover Boundary Thermostated Systems

Mejía‐Monasterio

Rondoni

2008

J Stat Phys

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We discuss the transient and steady state fluctuation relation for a mechanical system in contact with two deterministic thermostats at different temperatures. The system is a modified Lorentz gas in which the fixed scatterers exchange energy with the gas of particles, and the thermostats are modelled by two Nosé-Hoover thermostats applied at the boundaries of the system. The transient fluctuation relation, which holds only for a precise choice of the initial ensemble, is verified at all times, as expected. Times longer than the mesoscopic scale, needed for local equilibrium to be settled, are required if a different initial ensemble is considered. This shows how the transient fluctuation relation asymptotically leads to the steady state relation when, as explicitly checked in our systems, the condition found in [D.J. Searles, et al., J. Stat. Phys. 128, 1337(2007], for the validity of the steady state fluctuation relation, is verified. For the steady state fluctuations of the phase space contraction rate Λ and of the dissipation function Ω, a similar relaxation regime at shorter averaging times is found. The quantity Ω satisfies with good accuracy the fluctuation relation for times larger than the mesoscopic time scale; the quantity Λ appears to begin a monotonic convergence after such times. This is consistent with the fact that Ω and Λ differ by a total time derivative, and that the tails of the probability distribution function of Λ are Gaussian.

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Section: Introductionmentioning

confidence: 82%

“…3 These issues are closely related with the role played in the dynamics by the singularities of the total derivative which distinguishes Λ from Ω. This has been discussed in various papers, like [23,17,24,19]. The present paper is devoted to the investigation of such questions.…”

Section: Introductionmentioning

confidence: 90%

On the Fluctuation Relation for Nosé-Hoover Boundary Thermostated Systems

Mejía‐Monasterio

Rondoni

2008

J Stat Phys

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“…Out of equilibrium, ∆S = 0, and we will derive in Sec. 2.4.4 various fluctuation relations that have been extensively studied in recent years [17,18,19,20,21,22,23,24,25,26].…”

Section: Relation Between Path Probabilitiesmentioning

confidence: 99%

“…Altogether, we are led to propose the following transformation of the dynamical field x t and its associated auxiliary field ix t 26) complemented with the transformation of the discretisation parameter…”

Section: The Time-reversal Transformationmentioning

confidence: 99%

“…In this paper, we will use a model-independent field transformation in the path-integral formulation to show that the equilibrium fluctuation-dissipation theorems and the out-ofequilibrium fluctuation relations [17,18,19,20,21,22,23,24,25,26] hold for multiplicative white-noise Markov processes. Contrary to previous works for which the steady states were governed by non-equilibrium potentials, see e.g.…”

Section: Contents 1 Introductionmentioning

confidence: 99%

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Dynamical symmetries of Markov processes with multiplicative white noise

Aron¹,

Barci²,

Cugliandolo³

et al. 2016

J. Stat. Mech.

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We analyse various properties of stochastic Markov processes with multiplicative white noise. We take a single-variable problem as a simple example, and we later extend the analysis to the LandauLifshitz-Gilbert equation for the stochastic dynamics of a magnetic moment. In particular, we focus on the non-equilibrium transfer of angular momentum to the magnetization from a spin-polarised current of electrons, a technique which is widely used in the context of spintronics to manipulate magnetic moments. We unveil two hidden dynamical symmetries of the generating functionals of these Markovian multiplicative white-noise processes. One symmetry only holds in equilibrium and we use it to prove generic relations such as the fluctuation-dissipation theorems. Out of equilibrium, we take profit of the symmetry-breaking terms to prove fluctuation theorems. The other symmetry yields strong dynamical relations between correlation and response functions which can notably simplify the numerical analysis of these problems. Our construction allows us to clarify some misconceptions on multiplicative white-noise stochastic processes that can be found in the literature. In particular, we show that a first-order differential equation with multiplicative white noise can be transformed into an additive-noise equation, but that the latter keeps a non-trivial memory of the discretisation prescription used to define the former.

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