Experiments in Stochastic Thermodynamics: Short History and Perspectives

Ciliberto, S.

doi:10.1103/physrevx.7.021051

Cited by 303 publications

(377 citation statements)

References 172 publications

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“…where ξ(t) is a delta-correlated Gaussian white noise of zero mean and amplitude one. The Langevin equation (19) is numerically integrated (using Euler's numerical integration scheme). After a periodic steady-state has been reached, the statistics of T 1 , associated with the work exerted to the particle defined in the caption of Fig.…”

Section: S4 Arcsine Law For Periodically-driven Systems: Numerical Smentioning

confidence: 99%

“…Examples include conductance in disordered materials [6,7], chaotic dynamical systems [8], partial melting of polymers [9], quantum chaotic scattering [10] and generalized fractional Brownian processes [11]. Notably, the arcsine law (1) has also been explored in finance [12], where investment strategies can lead to a much smaller alternance of periods of gain and loss than one would expect based on naive arguments.Recent theory and experiments extended thermodynamics to mesoscopic systems that are driven away from equilibrium [13][14][15][16][17][18][19]. Mesoscopic systems operate at energies comparable with the thermal energy k B T , where k B is the Boltzmann constant and T is the temperature.…”

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confidence: 99%

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Arcsine Laws in Stochastic Thermodynamics

et al. 2018

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We show that the fraction of time that a thermodynamic current spends above its average value follows the arcsine law, a prominent result obtained by Lévy for Brownian motion. Stochastic currents with long streaks above or below their average are much more likely than those that spend similar fractions of time above and below their average. Our result is confirmed with experimental data from a Brownian Carnot engine. We also conjecture that two other random times associated with currents obey the arcsine law: the time a current reaches its maximum value and the last time a current crosses its average value. These results apply to, inter alia, molecular motors, quantum dots, and colloidal systems.

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Section: S4 Arcsine Law For Periodically-driven Systems: Numerical Smentioning

confidence: 99%

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confidence: 99%

Arcsine Laws in Stochastic Thermodynamics

et al. 2018

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“…In this paper, we experimentally and theoretically investigate the clean and rich system of a Brownian particle suspended in a complex, viscoelastic bath, a system which has in various forms been addressed before [5,[41][42][43][44], and which indeed shows unexplained non-equilibrium properties [45,46]. For example, the (transient) dynamics of a probe particle that has strongly perturbed its surrounding requires a theoretical description to account correctly for the stress release in the strained fluid, which is not avaliable.…”

Section: Introductionmentioning

confidence: 99%

Properties of a nonlinear bath: experiments, theory, and a stochastic Prandtl–Tomlinson model

et al. 2020

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A colloidal particle is a prominent example of a stochastic system, and, if suspended in a simple viscous liquid, very closely resembles the case of an ideal random walker. A variety of new phenomena have been observed when such colloid is suspended in a viscoelastic fluid instead, for example pronounced nonlinear responses when the viscoelastic bath is driven out of equilibrium. Here, using a micronsized particle in a micellar solution, we investigate in detail, how these nonlinear bath properties leave their fingerprints already in equilibrium measurements, for the cases where the particle is unconfined or trapped in a harmonic potential. We find that the coefficients in an effective linear (generalized) Langevin equation show intriguing inter-dependencies, which can be shown to arise only in nonlinear baths: for example, the friction memory can depend on the external potential that acts only on the colloidal particle (as recently noted in simulations of molecular tracers in water in (2017 Phys. Rev. X 7 041065)), it can depend on the mass of the colloid, or, in an overdamped setting, on its bare diffusivity. These inter-dependencies, caused by so-called fluctuation renormalizations, are seen in an exact small time expansion of the friction memory based on microscopic starting points. Using linear response theory, they can be interpreted in terms of microrheological modes of force-controlled or velocitycontrolled driving. The mentioned nonlinear markers are observed in our experiments, which are astonishingly well reproduced by a stochastic Prandtl-Tomlinson model mimicking the nonlinear viscoelastic bath. The pronounced nonlinearities seen in our experiments together with the good understanding in a simple theoretical model make this system a promising candidate for exploration of colloidal motion in nonlinear stochastic environments.

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“…This is a well-known aspect for stochastic dynamics of coupled components, each evolving at its own temperature (see, e.g. [26][27][28][29][30][31][32][33]). However, in the case at hand this nonzero current has a peculiar form due to the fact that the coupling term in equation (1) is a periodic function of the phase difference.…”

Section: Out-of-equilibrium Currentmentioning

confidence: 99%

Current-mediated synchronization of a pair of beating non-identical flagella

et al. 2019

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The basic phenomenology of experimentally observed synchronization (i.e. a stochastic phase locking) of identical, beating flagella of a biflagellate alga is known to be captured well by a minimal model describing the dynamics of coupled, limit-cycle, noisy oscillators (known as the noisy Kuramoto model). As demonstrated experimentally, the amplitudes of the noise terms therein, which stem from fluctuations of the rotary motors, depend on the flagella length. Here we address the conceptually important question which kind of synchrony occurs if the two flagella have different lengths such that the noises acting on each of them have different amplitudes. On the basis of a minimal model, too, we show that a different kind of synchrony emerges, and here it is mediated by a current carrying, steadystate; it manifests itself via correlated 'drifts' of phases. We quantify such a synchronization mechanism in terms of appropriate order parameters Q and  Q -for an ensemble of trajectories and for a single realization of noises of duration , respectively. Via numerical simulations we show that both approaches become identical for long observation times . This reveals an ergodic behavior and implies that a single-realization order parameter  Q is suitable for experimental analysis for which ensemble averaging is not always possible.

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Experiments in Stochastic Thermodynamics: Short History and Perspectives

Cited by 303 publications

References 172 publications

Arcsine Laws in Stochastic Thermodynamics

Arcsine Laws in Stochastic Thermodynamics

Properties of a nonlinear bath: experiments, theory, and a stochastic Prandtl–Tomlinson model

Current-mediated synchronization of a pair of beating non-identical flagella

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