Stochastic thermodynamics of resetting

Fuchs, Jaco; Goldt, Sebastian; Seifert, Udo

doi:10.1209/0295-5075/113/60009

Cited by 134 publications

(158 citation statements)

References 34 publications

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“…One may observe a very good agreement between theory (lines) and simulation (points). Figure 2 shows for two representative values of α < 1 a collapse of the simulation data for different times in accordance with the scaling form (17), with the lines showing the exact scaling function (18). One may note on crossing α = 3/4 the change in the behavior of P r,α<1 EW (h, t|0, 0) as h → 0, from being with a cusp to being divergent, as predicted by our exact results.…”

Section: Numerical Simulationssupporting

confidence: 70%

Resetting of fluctuating interfaces at power-law times

Gupta¹,

Nagar²

2016

J. Phys. A: Math. Theor.

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Abstract. What happens when the time evolution of a fluctuating interface is interrupted with resetting to a given initial configuration after random time intervals τ distributed as a power-law ∼ τ −(1+α) ; α > 0? For an interface of length L in one dimension, and an initial flat configuration, we show that depending on α, the dynamics in the limit L → ∞ exhibits a spectrum of rich long-time behavior. It is known that without resetting, the interface width grows unbounded with time as t β in this limit, where β is the so-called growth exponent characteristic of the universality class for a given interface dynamics. We show that introducing resetting induces for α > 1 and at long times fluctuations that are bounded in time. Corresponding to such a resetinduced stationary state is a distribution of fluctuations that is strongly non-Gaussian, with tails decaying as a power-law. The distribution exhibits a distinctive cuspy behavior for small argument, implying that the stationary state is out of equilibrium. For α < 1, on the contrary, resetting to the flat configuration is unable to counter the otherwise unbounded growth of fluctuations in time, so that the distribution of fluctuations remains time dependent with an ever-increasing width even at long times. Although stationary for α > 1, the width of the interface grows forever with time as a power-law for 1 < α < α (w) , and converges to a finite constant only for larger α, thereby exhibiting a crossover at α (w) = 1 + 2β. The time-dependent distribution of fluctuations for α < 1 exhibits for small argument another interesting crossover behavior, from cusp to divergence, across α (d) = 1 − β. We demonstrate these results by exact analytical results for the paradigmatic Edwards-Wilkinson (EW) dynamical evolution of the interface, and further corroborate our findings by extensive numerical simulations of interface models in the EW and the Kardar-Parisi-Zhang universality class.

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Section: Numerical Simulationssupporting

confidence: 70%

Resetting of fluctuating interfaces at power-law times

Gupta¹,

Nagar²

2016

J. Phys. A: Math. Theor.

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“…Interestingly, we find that this fluctuation relation leads to the second-law-like inequality found in Ref. [20].…”

Section: Discussionsupporting

confidence: 76%

“…al. [20], where the work and entropy production of resetting were identified, and a version of the second law that holds with resetting was derived.…”

Section: Discussionmentioning

confidence: 99%

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Integral fluctuation theorems for stochastic resetting systems

Pal

Rahav

2017

Phys. Rev. E

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We study the stochastic thermodynamics of resetting systems. Violation of microreversibility means that the well known derivations of fluctuations theorems break down for dynamics with resetting. Despite that we show that stochastic resetting systems satisfy two integral fluctuation theorems. The first is the Hatano-Sasa relation describing the transition between two steady states. The second integral fluctuation theorem involves a functional that includes both dynamical and thermodynamic contributions. We find that the second law-like inequality found by Fuchs et al. for resetting systems [EPL, 113, (2016)

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“…Also, the thermodynamic properties of resetting stochastic processes have been widely studied in [38], while in [39] general properties of restarted processes are analyzed by drawing an analogy with MichaelisMenten reactions.…”

Section: Introductionmentioning

confidence: 99%

Continuous-time random walks with reset events

2017

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In this paper, we consider a stochastic process that may experience random reset events which relocate the system to its starting position. We focus our attention on a one-dimensional, monotonic continuous-time random walk with a constant drift: the process moves in a fixed direction between the reset events, either by the effect of the random jumps, or by the action of a deterministic bias. However, the orientation of its motion is randomly determined after each restart. As a result of these alternating dynamics, interesting properties do emerge. General formulas for the propagator as well as for two extreme statistics, the survival probability and the mean first-passage time, are also derived. The rigor of these analytical results is verified by numerical estimations, for particular but illuminating examples.

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Stochastic thermodynamics of resetting

Cited by 134 publications

References 34 publications

Resetting of fluctuating interfaces at power-law times

Resetting of fluctuating interfaces at power-law times

Integral fluctuation theorems for stochastic resetting systems

Continuous-time random walks with reset events

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