Diffusion in a potential landscape with stochastic resetting

Pal, A.

doi:10.1103/physreve.91.012113

Cited by 193 publications

(174 citation statements)

References 19 publications

(20 reference statements)

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“…In the context of a target search process, the effect of partial absorption has been considered in [27]. Properties of non-equilibrium steady state for diffusion with resetting have been studied in the presence of a potential [28] or in a bounded domain [29]. Other generalizations include resetting to the current maximum of the Brownian particle [30], resetting in continuous-time random walks [31], in Lévy flights [25] etc.…”

Section: Introductionmentioning

confidence: 99%

Diffusion under time-dependent resetting

Pal

Kundu

Evans

2016

J. Phys. A: Math. Theor.

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271

319

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We study a Brownian particle diffusing under a time-modulated stochastic resetting mechanism to a fixed position. The rate of resetting r(t) is a function of the time t since the last reset event. We derive a sufficient condition on r(t) for a steady-state probability distribution of the position of the particle to exist. We derive the form of the steady-state distributions under some particular choices of r(t) and also consider the late time relaxation behavior of the probability distribution. We consider first passage time properties for the Brownian particle to reach the origin and derive a formula for the mean first passage time. Finally, we study optimal properties of the mean first passage time and show that a threshold function is at least locally optimal for the problem of minimizing the mean first passage time.

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Section: Introductionmentioning

confidence: 99%

Diffusion under time-dependent resetting

Pal

Kundu

Evans

2016

J. Phys. A: Math. Theor.

Self Cite

271

319

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“…One of the basic results of recent investigations of search with resetting [24][25][26] was to determine the conditions that optimize the search time. This resetting mechanism has also been quite fruitful conceptually and a variety of interesting consequences of resetting have been elucidated [27][28][29][30][31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Stochastic search with Poisson and deterministic resetting

Bhat¹,

Bacco²,

Redner³

2016

J. Stat. Mech.

137

136

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Abstract.We investigate a stochastic search process in one, two, and three dimensions in which N diffusing searchers that all start at x 0 seek a target at the origin. Each of the searchers is also reset to its starting point, either with rate r, or deterministically, with a reset time T . In one dimension and for a small number of searchers, the search time and the search cost are minimized at a non-zero optimal reset rate (or time), while for sufficiently large N , resetting always hinders the search. In general, a single searcher leads to the minimum search cost in one, two, and three dimensions. When the resetting is deterministic, several unexpected feature arise for N searchers, including the search time being independent of T for 1/T → 0 and the search cost being independent of N over a suitable range of N . Moreover, deterministic resetting typically leads to a lower search cost than in stochastic resetting.

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“…the time-reversal of resetting events). This simple observation means that stochastic dynamics with resetting can not satisfy detailed balance, and the system must therefore relax to a non-equilibrium steady state [5]. It has been noticed that the dynamics of relaxation to the steady-state can be quite unusual in the presence of resetting [7].…”

Section: Introductionmentioning

confidence: 99%

“…Dynamics with resetting, where a system is intermittently returned to a predetermined state, has been fascinating researchers from many fields and disciplines [1][2][3][4][5][6][7][8][9]. Indeed, dynamical systems with resetting have been employed as models for diverse situations such as searching for lost possessions, foraging for food in the wild, stochastic phenotype switching, optimal search algorithms, and random catastrophic events [10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

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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Diffusion in a potential landscape with stochastic resetting

Cited by 193 publications

References 19 publications

Diffusion under time-dependent resetting

Diffusion under time-dependent resetting

Stochastic search with Poisson and deterministic resetting

Integral fluctuation theorems for stochastic resetting systems

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