Reducing mean first passage times with intermittent confining potentials: a realization of resetting processes

Mercado-Vásquez, Gabriel; Boyer, Denis; Majumdar, Satya N.

doi:10.1088/1742-5468/ac8806

Cited by 8 publications

(4 citation statements)

References 51 publications

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“…The distribution is a doubleexponential-see equation (77). It is highly out of equilibrium as in that case, we showed that the effective temperature of the system diverges-see equation (87). The strongly passive limit τr ≪ τµ (β → ∞) is shown on the right panel.…”

Section: Stationary Distribution Of the Positionmentioning

confidence: 58%

“…The approach developed here based on Kesten variables is quite appealing and it would be nice to extend it in various directions. A first class of models where this approach could be useful are the 'potential resetting' problems, studied for instance in [86][87][88]. In these models, a single Brownian particle is subjected to an external confining potential that is switched on and off stochastically, as in the recent experiments on resetting using optical tweezers [52,53].…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Active particle in a harmonic trap driven by a resetting noise: an approach via Kesten variables

Guéneau,

Majumdar,

Schehr

2023

J. Phys. A: Math. Theor.

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We consider the statics and dynamics of a single particle trapped in a one-dimensional harmonic potential, and subjected to a driving noise with memory, that is represented by a resetting stochastic process. The finite memory of this driving noise makes the dynamics of this particle ``active''. At some chosen times (deterministic or random), the noise is reset to an arbitrary position and restarts its motion. We focus on two resetting protocols: periodic resetting, where the period is deterministic, and Poissonian resetting, where times between resets are exponentially distributed with a rate $r$. Between the different resetting epochs, we can express recursively the position of the particle. The random relation obtained takes a simple Kesten form that can be used to derive an integral equation for the stationary distribution of the position. We provide a detailed analysis of the distribution when the noise is a resetting Brownian motion. In this particular instance, we also derive a renewal equation for the full time dependent distribution of the position that we extensively study. These methods are quite general and can be used to study any process harmonically trapped when the noise is reset at random times.

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Section: Stationary Distribution Of the Positionmentioning

confidence: 58%

Section: Discussionmentioning

confidence: 99%

Active particle in a harmonic trap driven by a resetting noise: an approach via Kesten variables

Guéneau,

Majumdar,

Schehr

2023

J. Phys. A: Math. Theor.

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“…This seems to be more relevant in realistic situation. In experiments, one promising way to control a particle by an intermittent potential [57,58,100]. In the absence of external potential, the particle diffuses freely.…”

Section: Modelmentioning

confidence: 99%

Breakdown of arcsine law for resetting brownian motion

Yan,

Chen

2023

Phys. Scr.

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For a one-dimensional Brownian motion starting from the origin, the cumulative distribution of the occupation time V staying above the origin obeys the celebrated arcsine law. In this work, we show how the law is modified for a resetting Brownian motion, where the Brownian is reset to the position x r at random times but with a constant rate r. When x r is exactly equal to zero, we derive the exact expression of the probability distribution P r (V∣0, t) of V during time t, and the moments of V as functions of r and t. P r (V∣0, t) is always symmetric with respect to V = t/2 for arbitrary value of r, but the probability density of V at V = t/2 increases with the increase of r. Interestingly, P r (V∣0, t) at V = t/2 changes from a minimum to a local maximum at a critical value R * ≈ 0.742 338, where R = rt denotes the average number of resetting during time t. Moreover, we consider the case when x r is a random variable and is distributed by a function g(x r ), where g(x r ) is assumed to be symmetric with respect to zero and possesses its maximum at zero. We derive the general expressions of the moments of V when the variance of x r is low. The mean value of V is always equal to t/2, but the fluctuation in x r leads to an increase in the second and third moments of V. Our results provide a quantitative understanding of how stochastic resetting destroys the persistence of Brownian motion.

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“…Here a resetting trap is turned on, presumably at a random instance of time, in order to bring a particle to a prescribed position. This resetting scheme has been studied both in theory [52][53][54][55][56][57][58] and in recent experimental implementations of resetting using optical tweezers [27,59,60]. Other types of costs that do not necessarily correspond to thermodynamic quantities has also been considered recently [61,62].…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic work of partial resetting

Stølevik Olsen,

Gupta

2024

J. Phys. A: Math. Theor.

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Partial resetting, whereby a state variable $x(t)$ is reset at random times to a value $a x (t)$, $0\leq a \leq 1$, generalizes conventional resetting by introducing the resetting strength $a$ as a parameter. Partial resetting generates a broad family of non-equilibrium steady states (NESS) that interpolates between the conventional NESS at strong resetting ($a=0$) and a Gaussian distribution at weak resetting ($a \to 1$). Here such resetting processes are studied from a thermodynamic perspective, and the mean cost associated with maintaining such NESS are derived. The resetting phase of the dynamics is implemented by a resetting potential $\Phi(x)$ that mediates the resets in finite time. By working in an ensemble of trajectories with a fixed number of resets, we study both the steady-state properties of the propagator and its moments. The thermodynamic work needed to sustain the resulting NESS is then investigated. We find that different resetting traps can give rise to rates of work with widely different dependencies on the resetting strength $a$. Surprisingly, in the case of resets mediated by a harmonic trap with otherwise free diffusive motion, the asymptotic rate of work is insensitive to the value of $a$. For general anharmonic traps, the asymptotic rate of work can be either increasing or decreasing as a function of the strength $a$, depending on the degree of anharmonicity. Counter to intuition, the rate of work can therefore in some cases increase as the resetting becomes weaker $(a\to 1)$ although the work vanishes at $a=1$. Work in the presence of a background potential is also considered. Numerical simulations confirm our findings.

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Reducing mean first passage times with intermittent confining potentials: a realization of resetting processes

Cited by 8 publications

References 51 publications

Active particle in a harmonic trap driven by a resetting noise: an approach via Kesten variables

Active particle in a harmonic trap driven by a resetting noise: an approach via Kesten variables

Breakdown of arcsine law for resetting brownian motion

Thermodynamic work of partial resetting

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