On the Second Fluctuation–Dissipation Theorem for Nonequilibrium Baths

Maes, Christian

doi:10.1007/s10955-013-0904-8

Cited by 62 publications

(87 citation statements)

References 51 publications

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Section: The Problemsupporting

confidence: 84%

“…The relation between the noise covariance and the friction kernel is no longer that of the standard Einstein or second fluctuation-dissipation relation. That was already shown in [16] in the same context as the present paper but for Y t ≡ Y 0 fixed in time.The present paper is thus an extension of [16] for probe motion around (time-dependent) behavior. That requires also an extension of the presently existing results for linear response around nonequilibria.…”

supporting

confidence: 84%

“…which is different from the second fluctuation-dissipation relation valid for systems in contact with an equilibrium environment, [16,22,14,15,7]. The modification to the standard fluctuation-dissipation relation (cf.…”

Section: Second Fluctuation-dissipation Relationmentioning

confidence: 84%

“…The present paper is thus an extension of [16] for probe motion around (time-dependent) behavior. That requires also an extension of the presently existing results for linear response around nonequilibria.…”

Section: Friction and Noise For A Probe In A Nonequilibrium Fluidmentioning

confidence: 99%

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Friction and noise for a probe in a nonequilibrium fluid

Maes

Steffenoni

2015

Phys. Rev. E

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Abstract. We investigate the fluctuation dynamics of a probe around a deterministic motion induced by interactions with driven particles. The latter constitute the nonequilibrium medium in which the probe is immersed and is modelled as overdamped Langevin particle dynamics driven by nonconservative forces. The expansion that yields the friction and noise expressions for the reduced probe dynamics is based on linear response around a time-dependent nonequilibrium condition of the medium. The result contains an extension of the second fluctuation-dissipation relation between friction and noise for probe motion in a nonequilibrium fluid. The problemWhether the environment of a system is in equilibrium or is driven into a nonequilibrium condition is important for characterizing internal motions and reactions. In other words the reduced system dynamics will reflect whether the environment is driven or not.For example, the relation between noise and friction on the system need no longer be described via the standard second fluctuation-dissipation (or Einstein) relation, we cannot unambiguously speak about entropy fluxes into the environment in terms of heat as there would be no Clausius relation, and system fluctuations or noise level in general are not simply quantified by a reservoir temperature. The present paper takes up the challenge of characterizing such an effective dynamics for a probe in contact with a nonequilibrium medium. One should have in mind that the medium consists of active elements or driven particles themselves in contact with a big thermal equilibrium reservoir (like surrounding air or water). Combined, the medium and the heat bath make up the nonequilibrium fluid. The system is called a probe here, but it can in general also refer to a collective or with j = 1, . . . , N labeling the particles and subject to independent standard white noises ξ j t . The β denotes the inverse temperature of the background equilibrium reservoir but the particles are effectively driven by the nonconservative force F . For simplicity we have not introduced explicitly friction and mass parameters, keeping only λ (coupling) and β as parameters. The particle interaction is given through the potential Φ while the potential U depends on the position X t of the probe, thus representing the back-reaction of the probe on each particle. Other and different types of interaction between probe and medium are possible, e.g. in terms of their center of mass coordinate with a mean field type potential U ( j x j t − X t ), here not discussed and inessential for the present level of discussion. Keeping to (1.1) the probe dynamics itself iswhere we indicate by K X t ,Ẋ t other aspects of the probe motion in the fluid. Its mass M is obviously also an important parameter for separation of time-scales between probe and fluid particle motion.The equations (1.1) and (1.2) starting at t = 0 are the basic evolution equations representing the coupled dynamics of probe and fluid particles. Nonequilibrium works directly on the medium which is ...

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Section: The Problemsupporting

confidence: 84%

supporting

confidence: 84%

Section: Second Fluctuation-dissipation Relationmentioning

confidence: 84%

Section: Friction and Noise For A Probe In A Nonequilibrium Fluidmentioning

confidence: 99%

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Friction and noise for a probe in a nonequilibrium fluid

Maes

Steffenoni

2015

Phys. Rev. E

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“…From a viewpoint of non-equilibrium statistical mechanics, the essential step of the derivation is the calculation of the friction constant in terms of the time-correlation function. The formula (32), which is one of standard fluctuation-dissipation theorems, can be obtained by various methods. The advantage of our formulation is that we can obtain the nonlinear differential equation with the formula of the friction constant.…”

Section: Stochastic Thermodynamicsmentioning

confidence: 99%

Collective dynamics from stochastic thermodynamics

Sasa

2015

New J. Phys.

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From a viewpoint of stochastic thermodynamics, we derive equations that describe the collective dynamics near the order-disorder transition in the globally coupled XY model and near the synchronization-desynchronization transition in the Kuramoto model. A new way of thinking is to interpret the deterministic time evolution of a macroscopic variable as an external operation to a thermodynamic system. We then find that the irreversible work determines the equation for the collective dynamics. When analyzing the Kuramoto model, we employ a generalized concept of irreversible work which originates from a non-equilibrium identity associated with steady state thermodynamics.

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Brownian Particle in a Poisson‐Shot‐Noise Active Bath: Exact Statistics, Effective Temperature, and Inference

Di Bello,

Majumdar,

Marathe

et al. 2024

Annalen der Physik

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The dynamics of an overdamped Brownian particle in a thermal bath that contains a dilute solution of active particles is studied. The particle moves in a harmonic potential and experiences Poisson shot‐noise kicks with specified amplitude distribution due to moving active particles in the bath. From the Fokker–Planck equation for the particle dynamics, the stationary solution for the displacement distribution is derived along with the moments characterizing mean, variance, skewness, and kurtosis, as well as finite‐time first and second moments. An effective temperature is also computed through the fluctuation–dissipation theorem and show that equipartition theorem holds for all zero‐mean kick distributions, including those leading to non‐Gaussian stationary statistics. For the case of Gaussian‐distributed active kicks, a re‐entrant behavior from non‐Gaussian to Gaussian stationary states and a heavy‐tailed leptokurtic distribution across a wide range of parameters are found as seen in recent experimental studies. Further analysis reveals statistical signatures of the irreversible dynamics of the particle displacement in terms of the time asymmetry of cross‐correlation functions. Fruits of the work is the development of an compact inference scheme that may allow experimentalists to extract the rate and moments of underlying shot‐noise solely from the statistics the particle position.

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On the Second Fluctuation–Dissipation Theorem for Nonequilibrium Baths

Cited by 62 publications

References 51 publications

Friction and noise for a probe in a nonequilibrium fluid

Friction and noise for a probe in a nonequilibrium fluid

Collective dynamics from stochastic thermodynamics

Brownian Particle in a Poisson‐Shot‐Noise Active Bath: Exact Statistics, Effective Temperature, and Inference

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