Brownian motion under intermittent harmonic potentials

Santra, Ion; Das, Santanu; Nath, Sujit Kumar

doi:10.1088/1751-8121/ac12a0

Cited by 28 publications

(39 citation statements)

References 53 publications

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“…The stationary probabilities exist provided that α 0 > 0 [60]. While it is relatively easy to obtain these stationary probabilities in Fourier space, deriving a closedform analytic expression for the probability distribution in real space is highly nontrivial [30,61,62] (see also Appendix A). In what follows, we interestingly show that such an analytic form is not required for the calculation of the steady-state entropy production.…”

Section: Brownian Motion In An Intermittent Harmonic Potentialmentioning

confidence: 99%

“…2, we confirm numerically this result through: (1) the numerical integration of Eq. ( 26) using the stationary current derived from (see Appendix A and [30,62]) and (2) the analysis of single particle trajectories from the simulated underlying microscopic process governed by Eq. (2) (see Appendix B for further numerical details).…”

Section: Brownian Motion In An Intermittent Harmonic Potentialmentioning

confidence: 99%

“…(12) and (13). For completeness, we rederive here shortly the steady-state distributions following the derivations found in [30,62].…”

Section: Appendix a Steady-state Densities For Brownian Motion In An ...mentioning

confidence: 99%

“…As shown in Ref. [30], it is possible to obtain exact expressions for the steady-state distribution in some asymptotic regimes. In particular, in the limit where the switching rate is very small compared to the confining potential strength, k α 0 , the steady-state distribution is given by…”

Section: Appendix a Steady-state Densities For Brownian Motion In An ...mentioning

confidence: 99%

“…Furthermore, Brownian motion in an intermittent harmonic confining potential represents a realistic implementation of stochastic resetting [30][31][32][33][34]. Originally introduced to allow Brownian dynamics to reach a nonequilibrium stationary state (NESS) at long times [34,35], stochastic resetting has been under intense scrutiny over the last decade partly due to its non-trivial impact on first-passage statistics [35,36] and has imposed itself as a pillar of nonequilibrium statistical mechanics.…”

Section: Introductionmentioning

confidence: 99%

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Non-equilibrium thermodynamics of diffusion in fluctuating potentials

Alston,

Cocconi,

Bertrand

2022

Preprint

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A positive rate of entropy production at steady state is a distinctive feature of truly non-equilibrium processes. Exact results, while being often limited to simple models, offer a unique opportunity to explore the thermodynamic features of these processes in full details. Here we derive analytical results for the steady-state rate of entropy production in single particle systems driven away from equilibrium by the fluctuations of an external potential of arbitrary shapes. Subsequently, we provide exact results for a diffusive particle in a harmonic trap whose potential stiffness varies in time according to both discrete and continuous Markov processes. In particular, studying the case of a fully intermittent potential allows us to introduce an effective model of stochastic resetting for which it is possible to obtain finite non-negative entropy production. Altogether, this work lays the foundation for a non-equilibrium thermodynamic theory of fluctuating potentials, with immediate applications to stochastic resetting processes, fluctuations in optical traps and fluctuating interactions in living systems.

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Section: Brownian Motion In An Intermittent Harmonic Potentialmentioning

confidence: 99%

Section: Brownian Motion In An Intermittent Harmonic Potentialmentioning

confidence: 99%

“…(12) and (13). For completeness, we rederive here shortly the steady-state distributions following the derivations found in [30,62].…”

Section: Appendix a Steady-state Densities For Brownian Motion In An ...mentioning

confidence: 99%

Section: Appendix a Steady-state Densities For Brownian Motion In An ...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Non-equilibrium thermodynamics of diffusion in fluctuating potentials

Alston,

Cocconi,

Bertrand

2022

Preprint

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Work fluctuations for diffusion dynamics submitted to stochastic return

Gupta

Plata

2022

New J. Phys.

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Returning a system to a desired state under a force field involves a thermodynamic cost, i.e., {\it work}. This cost fluctuates for a small-scale system from one experimental realization to another. We introduce a general framework to determine the work distribution for returning a system facilitated by a confining potential with its minimum at the restart location. The general strategy, based on average over \textit{resetting pathways}, constitutes a robust method to gain access to the statistical information of observables from resetting systems. We exploit paradigmatic setups, where explicit computations are attainable, to illustrate the theory. Numerical simulations validate our theoretical predictions. For some of these examples, a non-trivial behavior of the work fluctuations opens a door to optimization problems. Specifically, work fluctuations can be minimized by an appropriate tuning of the return rate.

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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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Brownian motion under intermittent harmonic potentials

Cited by 28 publications

References 53 publications

Non-equilibrium thermodynamics of diffusion in fluctuating potentials

Non-equilibrium thermodynamics of diffusion in fluctuating potentials

Work fluctuations for diffusion dynamics submitted to stochastic return

Breakdown of arcsine law for resetting brownian motion

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