Integral fluctuation theorems for stochastic resetting systems

Pal, A.; Rahav, Saar

doi:10.1103/physreve.96.062135

Cited by 85 publications

(65 citation statements)

References 58 publications

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“…The resetting entropy production rate was derived for this system with space dependent resetting rate r(x) to resetting position X ṙ S reset = dx r(x)p(x) ln p(x) p Xr (8.1) and from this a second law of thermodynamics including resetting was proposed (see also [152]). Building on the identification of entropy change due to resetting, Pal and Rahav [153] considered how integral fluctuation theorems apply to resetting problems. The integral theorems may be thought of as generalising the second law to equalities involving averages over fluctuations [155].…”

Section: Thermodynamics Of Resetting and Integral Theoremsmentioning

confidence: 99%

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Stochastic resetting and applications

Evans

Majumdar

Schehr

2020

J. Phys. A: Math. Theor.

531

600

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In this Topical Review we consider stochastic processes under resetting, which have attracted a lot of attention in recent years. We begin with the simple example of a diffusive particle whose position is reset randomly in time with a constant rate r, which corresponds to Poissonian resetting, to some fixed point (e.g. its initial position). This simple system already exhibits the main features of interest induced by resetting: (i) the system reaches a nontrivial nonequilibrium stationary state (ii) the mean time for the particle to reach a target is finite and has a minimum, optimal, value as a function of the resetting rate r. We then generalise to an arbitrary stochastic process (e.g. Lévy flights or fractional Brownian motion) and non-Poissonian resetting (e.g. power-law waiting time distribution for intervals between resetting events). We go on to discuss multiparticle systems as well as extended systems, such as fluctuating interfaces, under resetting. We also consider resetting with memory which implies resetting the process to some randomly selected previous time. Finally we give an overview of recent developments and applications in the field.

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Section: Thermodynamics Of Resetting and Integral Theoremsmentioning

confidence: 99%

“…They showed how the Hatano-Sasa integral fluctuation theorem [154] which pertains to nonequilibrium steady states is also valid for systems with resetting. Further integral theorems have been considered in [153,156].…”

Section: Thermodynamics Of Resetting and Integral Theoremsmentioning

confidence: 99%

Stochastic resetting and applications

Evans

Majumdar

Schehr

2020

J. Phys. A: Math. Theor.

531

600

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“…Stochastic resetting is a mechanism in which the system undergoes a stochastic dynamics in the state space as well as stochastically resets to a prescribed location with a given transition rate (i.e., a unidirectional process) [16,25,26,[49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64]. These resetting transitions involve jumps of the system into given locations and can be called the controlled transitions (i.e., these can be tuned from external sources).…”

Section: Application: Stochastic Resettingmentioning

confidence: 99%

Entropy production in systems with unidirectional transitions

Busiello

Gupta

Maritan

2020

Phys. Rev. Research

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The entropy production is one of the most essential features for systems operating out of equilibrium. The formulation for discrete-state systems goes back to the celebrated Schnakenberg's work and hitherto can be carried out when for each transition between two states also the reverse one is allowed. Nevertheless, several physical systems may exhibit a mixture of both unidirectional and bidirectional transitions, and how to properly define the entropy production in this case is still an open question. Here, we present a solution to such a challenging problem. The average entropy production can be consistently defined, employing a mapping that preserves the average fluxes, and its physical interpretation is provided. We describe a class of stochastic systems composed of unidirectional links forming cycles and detailed-balanced bidirectional links, showing that they behave in a pseudo-deterministic fashion. This approach is applied to a system with time-dependent stochastic resetting. Our framework is consistent with thermodynamics and leads to some intriguing observations on the relation between the arrow of time and the average entropy production for resetting events.

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“…Stochastic motion with stochastic resetting is of considerable interest due to its broad applicability in statistical [1][2][3][4][5][6][7], chemical [8][9][10][11][12], and biological physics [13,14]; and due to its importance in computer science [15,16], computational physics [17,18], population dynamics [19][20][21], queuing theory [22][23][24] and the theory of search and first-passage [25][26][27]. Particularly, in statistical physics, such motion has become a focal point of recent studies owing to the rich non-equilibrium [2][3][4][5][6][28][29][30] and first-passage [31][32][33][34][35][36] phenomena it displays.…”

Section: Introductionmentioning

confidence: 99%

Invariants of motion with stochastic resetting and space-time coupled returns

2019

Self Cite

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Motion under stochastic resetting serves to model a myriad of processes in physics and beyond, but in most cases studied to date resetting to the origin was assumed to take zero time or a time decoupled from the spatial position at the resetting moment. However, in our world, getting from one place to another always takes time and places that are further away take more time to be reached. We thus set off to extend the theory of stochastic resetting such that it would account for this inherent spatio-temporal coupling. We consider a particle that starts at the origin and follows a certain law of stochastic motion until it is interrupted at some random time. The particle then returns to the origin via a prescribed protocol. We study this model and surprisingly discover that the shape of the steady-state distribution which governs the stochastic motion phase does not depend on the return protocol. This shape invariance then gives rise to a simple, and generic, recipe for the computation of the full steady state distribution. Several case studies are analyzed and a class of processes whose steady state is completely invariant with respect to the speed of return is highlighted. For processes in this class we recover the same steady-state obtained for resetting with instantaneous returns-irrespective of whether the actual return speed is high or low. Our work significantly extends previous results on motion with stochastic resetting and is expected to find various applications in statistical, chemical, and biological physics.

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Integral fluctuation theorems for stochastic resetting systems

Cited by 85 publications

References 58 publications

Stochastic resetting and applications

Stochastic resetting and applications

Entropy production in systems with unidirectional transitions

Invariants of motion with stochastic resetting and space-time coupled returns

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