Non-equilibrium thermodynamics of diffusion in fluctuating potentials

Alston, Henry; Cocconi, Luca; Bertrand, Thibault

doi:10.1088/1751-8121/ac726b

Cited by 9 publications

(7 citation statements)

References 82 publications

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“…which were obtained in [40]. With these results and by using equation (39), we can calculate the leading order S (0) for the semi-infinite line,…”

Section: V-shaped Potentialmentioning

confidence: 83%

“…The NESSs and the diffusion properties that emerge in stochastically switching harmonic potentials have been studied for Brownian particles along different schemes [34,36], as well as for Lévy walks [37]. The work distribution [38] and entropy production have also been explored [39]. Notwithstanding these advances, the properties of first passage times in fluctuating potentials remain little understood.…”

Section: Introductionmentioning

confidence: 99%

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

Mercado-Vásquez¹,

Boyer²,

Majumdar³

2022

J. Stat. Mech.

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During a random search, resetting the searcher’s position from time to time to the starting point often reduces the mean completion time of the process. Although many different resetting models have been studied over the past ten years, only a few can be physically implemented. Here we study theoretically a protocol that can be realised experimentally and which exhibits unusual optimization properties. A Brownian particle is subject to an arbitrary confining potential v(x) that is switched on and off intermittently at fixed rates. Motion is constrained between an absorbing wall located at the origin and a reflective wall. When the walls are sufficiently far apart, the interplay between free diffusion during the ‘off’ phases and attraction toward the potential minimum during the ‘on’ phases give rise to rich behaviours, not observed in ideal resetting models. For potentials of the form v(x) = k|x − x 0| n /n, with n > 0, the switch-on and switch-off rates that minimise the mean first passage time (MFPT) to the origin undergo a continuous phase transition as the potential stiffness k is varied. When k is above a critical value k c, potential intermittency enhances the target encounter: the minimal MFPT is lower than the Kramer time and is attained for a non-vanishing pair of switching rates. We focus on the harmonic case n = 2, extending previous results for the piecewise linear potential (n = 1) in unbounded domains. We also study the non-equilibrium stationary states emerging in this process.

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“…which were obtained in [40]. With these results and by using equation (39), we can calculate the leading order S (0) for the semi-infinite line,…”

Section: V-shaped Potentialmentioning

confidence: 83%

Section: Introductionmentioning

confidence: 99%

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

Mercado-Vásquez¹,

Boyer²,

Majumdar³

2022

J. Stat. Mech.

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“…( 1), when the force due to the potential is aligned with the particle's own self-propulsion speed v, similarly to RnT particles in a harmonic potential [9]. Starting from the Gibbs-Shannon entropy [57], we take a well-established approach to obtain an exact expression for the entropy production rate at stationarity [10,52,58].…”

Section: Entropy Productionmentioning

confidence: 99%

“…At this point, we separate the time derivative of the entropy into the contributions Ṡ(t) = Ṡint (t) − Ṡext (t) and identify the positive-definite terms in Eq. ( 13) as those corresponding to the internal entropy production rate of the system Ṡint (t) [10,44,58]. We thus have…”

Section: Entropy Productionmentioning

confidence: 99%

Run-and-tumble motion in a linear ratchet potential: analytic solution, power extraction and first-passage properties

Roberts¹,

Zhen²

2023

Preprint

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We explore the properties of a system of run-and-tumble (RnT) particles moving in a piecewiselinear "ratchet" potential, and subject to non-negligible diffusion, by deriving exact analytical results for its steady-state probability density, current, entropy production rate, power output, and thermodynamic efficiency. The current, and thus the extractable power and efficiency, have non-monotonic dependencies on the diffusion strength, ratchet height, and particle self-propulsion speed, peaking at finite values in each case. In the case where the particles' self-propulsion is completely suppressed by the force from the ratchet, and thus a current can be generated only by diffusion-mediated barrier crossings, the system's entropy production rate remains finite in the limit of vanishing diffusion. In the final part of this work, we consider RnT motion in a linear ratchet potential on a bounded interval, allowing the derivation of mean first-passage times and splitting probabilities for different boundary and initial conditions. The present work resides at the interface of exactly solvable models of run-and-tumble motion and the study of work extraction from active matter by providing exact expressions pertaining to the feasibility and future design of active engines. Our results are in agreement with Monte Carlo simulations.

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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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Non-equilibrium thermodynamics of diffusion in fluctuating potentials

Cited by 9 publications

References 82 publications

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

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

Run-and-tumble motion in a linear ratchet potential: analytic solution, power extraction and first-passage properties

Thermodynamic work of partial resetting

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