Effective temperature in nonequilibrium steady states of Langevin systems with a tilted periodic potential

We discuss fluctuation relations in simple cases of non-equilibrium Langevin dynamics. In particular, we show that close to non-equilibrium steady states with non-vanishing probability currents some of these relations reduce to a modified version of the fluctuation-dissipation theorem. The latter may be interpreted as the equilibrium-like relation in the reference frame moving with the mean local velocity determined by the probability current.

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“…[42,14,41,25,23,44]. For such systems, we show a modified fluctuation-dissipation theorem (MFDT) that may be written in the form…”

Section: Introductionmentioning

confidence: 99%

Fluctuation relations in simple examples of non-equilibrium steady states

2008

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“…This is essentially a consequence of detailed balance and the role of the partition function as a moment-generating function, and thus such relations cannot be readily extended to nonequilibrium steady states. However, it has recently been shown that certain FDRs can be extended to far-from equilibrium steady states by use of an effective temperature [43,44]. Here we will therefore consider whether the nonequilibrium susceptibility and the scaled variance of the dynamic order parameter can be related aŝ…”

Section: Applicability Of a Fluctuation-dissipation Relationmentioning

confidence: 99%

Conjugate field and fluctuation-dissipation relation for the dynamic phase transition in the two-dimensional kinetic Ising model

et al. 2007

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The two-dimensional kinetic Ising model, when exposed to an oscillating applied magnetic field, has been shown to exhibit a nonequilibrium, second-order dynamic phase transition (DPT), whose order parameter Q is the period-averaged magnetization. It has been established that this DPT falls in the same universality class as the equilibrium phase transition in the two-dimensional Ising model in zero applied field. Here we study for the first time the scaling of the dynamic order parameter with respect to a nonzero, period-averaged, magnetic 'bias' field, H b , for a DPT produced by a square-wave applied field. We find evidence that the scaling exponent,

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“…(1) is not necessarily fulfilled out of equilibrium and violations are observed in a variety of systems such as glassy materials [1,2,3,4,5], granular matter [6], and biophysical systems [7]. This motivated a theoretical work devoted to a search of a general framework describing FD relations, see the review [8] or [9,10,11,12,13,14] for recent attempts in simple stochastic systems. In the same spirit, a modified fluctuation-dissipation theorem (MFDT) has been recently formulated for a non-equilibrium steady dynamics governed by the Langevin equation with nonconservative forces [15].…”

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Experimental Verification of a Modified Fluctuation-Dissipation Relation for a Micron-Sized Particle in a Nonequilibrium Steady State

et al. 2009

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A modified fluctuation-dissipation-theorem (MFDT) for a non-equilibrium steady state (NESS) is experimentally checked by studying the position fluctuations of a colloidal particle whose motion is confined in a toroidal optical trap. The NESS is generated by means of a rotating laser beam which exerts on the particle a sinusoidal conservative force plus a constant non-conservative one. The MFDT is shown to be perfectly verified by the experimental data. It can be interpreted as an equilibrium-like fluctuation-dissipation relation in the Lagrangian frame of the mean local velocity of the particle.The validity of the fluctuation-dissipation theorem (FDT) in systems out of thermal equilibrium has been the subject of intensive study during the last years. We recall that for a system in equilibrium with a thermal bath at temperature T the FDT establishes a simple relation between the 2-time correlation function C(t − s) of a given observable and the linear response function R(t − s) of this observable to a weak external perturbationHowever, Eq. (1) is not necessarily fulfilled out of equilibrium and violations are observed in a variety of systems such as glassy materials [1,2,3,4,5], granular matter [6], and biophysical systems [7]. This motivated a theoretical work devoted to a search of a general framework describing FD relations, see the review [8] or [9,10,11,12,13,14] for recent attempts in simple stochastic systems. In the same spirit, a modified fluctuation-dissipation theorem (MFDT) has been recently formulated for a non-equilibrium steady dynamics governed by the Langevin equation with nonconservative forces [15]. In particular, this MFDT holds for the overdamped motion of a particle on a circle, with angular position θ, in the presence of a periodic potential H(θ) = H(θ + 2π) and a constant non-conservative force Fθwhere ζ is a white noise term of mean ζ t = 0 and covariance ζ t ζ s = 2Dδ(t − s), with D the (bare) diffusivity. This is a system that may exhibit an increase in the effective diffusivity [16,17]. Here, we shall study the dynamical non-equilibrium steady state (NESS) reached for observables that depend only on the particle position on the circle so are periodic functions of the angle θ. Such a state corresponds to a constant non-vanishing probability current j along the circle and a periodic invariant probability density function ρ 0 (θ) that allow us to define a mean local velocity v 0 (θ) = j/ρ 0 (θ). This is the average velocity of the particle at θ. For a stochastic system in NESS evolving according to Eq. (2), the MFDT reads for t ≥ swhere the 2-time correlation of a given observable O(θ) is defined byand the linear response function to a δ-perturbation of the conjugated variable h t is given by the functional derivativeIn Eq. (5), ... h denotes the average in the perturbed time-dependent state obtained from the NESS by replacing H(θ) in Eq. (2) by H(θ) − h t O(θ). It reduces for h = 0 to the NESS average ... 0 . In Eq. (3), the correlation b(t − s) is given byThis new term takes into accoun...

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Effective temperature in nonequilibrium steady states of Langevin systems with a tilted periodic potential

Cited by 63 publications

References 13 publications

Fluctuation relations in simple examples of non-equilibrium steady states

Fluctuation relations in simple examples of non-equilibrium steady states

Conjugate field and fluctuation-dissipation relation for the dynamic phase transition in the two-dimensional kinetic Ising model

Experimental Verification of a Modified Fluctuation-Dissipation Relation for a Micron-Sized Particle in a Nonequilibrium Steady State

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