Exact distributions of currents and frenesy for Markov bridges

Roldán, Édgar; Vivo, Pierpaolo

doi:10.1103/physreve.100.042108

Cited by 31 publications

(18 citation statements)

References 97 publications

(123 reference statements)

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“…This model has also be investigated for N = 3 in Ref. [36]. We assume that the initial occupation probabilities are p 0 i = 1/N , which is the steady state of Eq.…”

Section: B Demonstration: Markov Chain Modelmentioning

confidence: 99%

Fluctuation–response inequality out of equilibrium

Dechant

Sasa

2020

Proc. Natl. Acad. Sci. U.S.A.

135

109

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We present a new approach to response around arbitrary out-of-equilibrium states in the form of a fluctuation-response inequality (FRI). We study the response of an observable to a perturbation of the underlying stochastic dynamics. We find that magnitude of the response is bounded from above by the fluctuations of the observable in the unperturbed system and the Kullback-Leibler divergence between the probability densities describing the perturbed and unperturbed system. This establishes a connection between linear response and concepts of information theory. We show that in many physical situations, the relative entropy may be expressed in terms of physical observables. As a direct consequence of this FRI, we show that for steady state particle transport, the differential mobility is bounded by the diffusivity. For a "virtual" perturbation proportional to the local mean velocity, we recover the thermodynamic uncertainty relation (TUR) for steady state transport processes. Finally, we use the FRI to derive a generalization of the uncertainty relation to arbitrary dynamics, which involves higher-order cumulants of the observable. We provide an explicit example, in which the TUR is violated but its generalization is satisfied with equality. arXiv:1804.08250v3 [cond-mat.stat-mech]

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“…This model has also be investigated for N = 3 in Ref. [36]. We assume that the initial occupation probabilities are p 0 i = 1/N , which is the steady state of Eq.…”

Section: B Demonstration: Markov Chain Modelmentioning

confidence: 99%

Fluctuation–response inequality out of equilibrium

Dechant

Sasa

2020

Proc. Natl. Acad. Sci. U.S.A.

135

109

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“…We refer for the following to [45,47] for more examples and corresponding additional fluctuation symmetries. Large deviations of time-symmetric activities have for example been considered in [48,51,132].…”

Section: A Symmetriesmentioning

confidence: 99%

“…New nonequilibrium effects due to a nontrivial frenetic contribution may only start at second order around equilibrium. We refer to the recent [51] for more frenetic symmetries.…”

Section: A Symmetriesmentioning

confidence: 99%

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Frenesy: Time-symmetric dynamical activity in nonequilibria

Maes

2020

Physics Reports

120

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We review the concept of dynamical ensembles in nonequilibrium statistical mechanics as specified from an action functional or Lagrangian on spacetime. There, under local detailed balance, the breaking of time-reversal invariance is quantified via the entropy flux, and we revisit some of the consequences for fluctuation and response theory. Frenesy is the time-symmetric part of the path-space action with respect to a reference process. It collects the variable quiescence and dynamical activity as function of the system's trajectory, and as has been introduced under different forms in studies of nonequilibria. We discuss its various realizations for physically inspired Markov jump and diffusion processes and why it matters a good deal for nonequilibrium physics. This review then serves also as an introduction to the exploration of frenetic contributions in nonequilibrium phenomena.

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“…It remains an open question to investigate whether the power optimization with the bath correlation time can be further discussed in relation with the frenetic aspects of nonequilibria [17,18,81,82], and whether this result applies to a broader class of systems. To serve an appetizer to this challenging task, we show in Fig.…”

Section: Discussionmentioning

confidence: 99%

Energetics of critical oscillators in active bacterial baths

Gopal,

Roldán,

Ruffo

2020

Preprint

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We investigate the nonequilibrium energetics near a critical point of a non-linear driven oscillator immersed in an active bacterial bath. At the critical point, we reveal a scaling exponent of the average power Ẇ ∼ (D a /τ ) 1/4 where D a is the effective diffusivity and τ the correlation time of the bacterial bath described by a Gaussian colored noise. Other features that we investigate are the average stationary power and the variance of the work both below and above the saddle-node bifurcation. Above the bifurcation, the average power attains an optimal, minimum value for finite τ that is below its zero-temperature limit. Furthermore, we reveal a finite-time uncertainty relation for active matter which leads to values of the Fano factor of the work that can be below 2k B T eff , with T eff the effective temperature of the oscillator in the bacterial bath. We analyze different Markovian approximations to describe the nonequilibrium stationary state of the system. Finally, we illustrate our results in the experimental context by considering the example of driven colloidal particles in periodic optical potentials within a E. Coli bacterial bath.

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Exact distributions of currents and frenesy for Markov bridges

Cited by 31 publications

References 97 publications

Fluctuation–response inequality out of equilibrium

Fluctuation–response inequality out of equilibrium

Frenesy: Time-symmetric dynamical activity in nonequilibria

Energetics of critical oscillators in active bacterial baths

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