Breakdown of Gallavotti-Cohen symmetry for stochastic dynamics

Harris, Rosemary J.; Rákos, A.; Schütz, Gunter M.

doi:10.1209/epl/i2006-10102-1

Cited by 74 publications

(115 citation statements)

References 29 publications

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“…The leading contribution to the LDF then comes from the singularity, which induces an exponential tail in the pdf. This issue is now well documented in the literature, both theoretically [14][15][16][17][18][19][20][21][22][23][24] and experimentally [25][26][27]. In consequence, while the three observables βW t , βQ t , and Σ t have the same expectation value, their LDFs may differ.…”

Section: Model and Observablesmentioning

confidence: 94%

Stochastic thermodynamics of Langevin systems under time-delayed feedback control. II. Nonequilibrium steady-state fluctuations

2017

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This paper is the second in a series devoted to the study of Langevin systems subjected to a continuous time-delayed feedback control. The goal of our previous paper [Phys. Rev. E 91, 042114 (2015)] was to derive second-law-like inequalities that provide bounds to the average extracted work. Here we study stochastic fluctuations of time-integrated observables such as the heat exchanged with the environment, the extracted work, or the (apparent) entropy production. We use a path-integral formalism and focus on the long-time behavior in the stationary cooling regime, stressing the role of rare events. This is illustrated by a detailed analytical and numerical study of a Langevin harmonic oscillator driven by a linear feedback.

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Section: Model and Observablesmentioning

confidence: 94%

Stochastic thermodynamics of Langevin systems under time-delayed feedback control. II. Nonequilibrium steady-state fluctuations

2017

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“…This gives rise to exponential tails in the pdf of Q and is signaled by the presence of singularities in the corresponding characteristic function. Such temporal "boundary" effects that take place in systems with unbounded potentials are now well-documented, both theoretically [6][7][8][9][10][11][12][13][14][15][16][17] and experimentally [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Heat fluctuations for underdamped Langevin dynamics

Rosinberg¹,

Tarjus²,

Munakata³

2016

EPL

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Fluctuation theorems play a central role in nonequilibrium physics and stochastic thermodynamics. Here we derive an integral fluctuation theorem for the dissipated heat in systems governed by an underdamped Langevin dynamics. We show that this identity may be used to predict the occurrence of extreme events leading to exponential tails in the probability distribution functions of the heat and related quantities.

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“…Therefore, in the long-time limit, our conventional wisdom may lead us to expect that the PDF's of Q d and Q i will lose all initial memory, thus become independent of β. However, it has been noticed in various examples [23,24,25,28,37] that the effect of initial conditions can remain in the tail of the PDF's (rare-event region) even in the infinite-time limit.…”

Section: Equilibration Process Of a Brownian Particlementioning

confidence: 99%

Modified saddle-point integral near a singularity for the large deviation function

2013

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Abstract. Long-time-integrated quantities in stochastic processes, in or out of equilibrium, usually exhibit rare but huge fluctuations. Work or heat production is such a quantity, of which the probability distribution function displays an exponential decay characterized by the large deviation function (LDF). The LDF is often deduced from the cumulant generating function through the inverse Fourier transformation. The saddle-point integration method is a powerful technique to obtain the asymptotic results in the Fourier integral, but a special care should be taken when the saddle point is located near a singularity of the integrand. In this paper, we present a modified saddle-point method to handle such a difficulty efficiently. We investigate the dissipated and injected heat production in equilibration processes with various initial conditions, as an example, where the generating functions contain branch-cut singularities as well as power-law ones. Exploiting the new modified saddle-point integrations, we obtain the leading finite-time corrections for the LDF's, which are confirmed by numerical results.

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Breakdown of Gallavotti-Cohen symmetry for stochastic dynamics

Cited by 74 publications

References 29 publications

Stochastic thermodynamics of Langevin systems under time-delayed feedback control. II. Nonequilibrium steady-state fluctuations

Stochastic thermodynamics of Langevin systems under time-delayed feedback control. II. Nonequilibrium steady-state fluctuations

Heat fluctuations for underdamped Langevin dynamics

Modified saddle-point integral near a singularity for the large deviation function

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