Inequivalence of nonequilibrium path ensembles: the example of stochastic bridges

Szavits-Nossan, Juraj; Evans, Martin R.

doi:10.1088/1742-5468/2015/12/p12008

Cited by 38 publications

(38 citation statements)

References 63 publications

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“…Here, we find "temporal condensates" in the form of trajectories for the fluctuations of A τ that are localized in time compared to τ and whose height scales with τ . A related condensation was reported recently in the context of sums of random variables, which can be dominated in some cases by a single, extensive or "giant" value [69][70][71][72][73][74].…”

supporting

confidence: 53%

Anomalous Scaling of Dynamical Large Deviations

Nickelsen

Touchette

2018

Phys. Rev. Lett.

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The typical values and fluctuations of time-integrated observables of nonequilibrium processes driven in steady states are known to be characterized by large deviation functions, generalizing the entropy and free energy to nonequilibrium systems. The definition of these functions involves a scaling limit, similar to the thermodynamic limit, in which the integration time τ appears linearly, unless the process considered has long-range correlations, in which case τ is generally replaced by τ^{ξ} with ξ≠1. Here, we show that such an anomalous power-law scaling in time of large deviations can also arise without long-range correlations in Markovian processes as simple as the Langevin equation. We describe the mechanism underlying this scaling using path integrals and discuss its physical consequences for more general processes.

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confidence: 53%

Anomalous Scaling of Dynamical Large Deviations

Nickelsen

Touchette

2018

Phys. Rev. Lett.

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“…Equation (B7) also represents the variance of a Brownian bridge (see, e.g., Refs. [84,88]). For a Dirichlet profile whose area is constrained to vanish, the averaged path results instead as…”

Section: Dirichlet Boundary Conditionsmentioning

confidence: 99%

First-passage dynamics of linear stochastic interface models: numerical simulations and entropic repulsion effect

Groß¹

2018

J. Stat. Mech.

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A fluctuating interfacial profile in one dimension is studied via Langevin simulations of the Edwards-Wilkinson equation with non-conserved noise and the Mullins-Herring equation with conserved noise. The profile is subject to either periodic or Dirichlet (no-flux) boundary conditions. We determine the noise-driven time-evolution of the profile between an initially flat configuration and the instant at which the profile reaches a given height M for the first time. The shape of the averaged profile agrees well with the prediction of weak-noise theory (WNT), which describes the most-likely trajectory to a fixed first-passage time. Furthermore, in agreement with WNT, on average the profile approaches the height M algebraically in time, with an exponent that is essentially independent of the boundary conditions. However, the actual value of the dynamic exponent turns out to be significantly smaller than predicted by WNT. This "renormalization" of the exponent is explained in terms of the entropic repulsion exerted by the impenetrable boundary on the fluctuations of the profile around its most-likely path. The entropic repulsion mechanism is analyzed in detail for a single (fractional) Brownian walker, which describes the anomalous diffusion of a tagged monomer of the interface as it approaches the absorbing boundary. The present study sheds light on the accuracy and the limitations of the weak-noise approximation for the description of the full first-passage dynamics.

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“…An important observation is that the bounds on fluctuations of a counting observable and its FPTs are controlled by the average dynamical activity, in analogy to the role played by the entropy production in the case of currents [1,13]. We hope these results will add to the growing body of work applying large deviation ideas and methods to the study of dynamics in driven systems [29][30][31][32][33][34][35][36][37][38][39][40][41], glasses [25,[42][43][44][45][46][47], protein folding and signaling networks [48][49][50][51], open quantum systems [52][53][54][55][56][57][58][59][60][61][62][63][64], and many other problems in nonequilibrium [65][66][67][68][69][70][71][72].…”

Section: Introductionmentioning

confidence: 98%

Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables

2017

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Recent large deviation results have provided general lower bounds for the fluctuations of time-integrated currents in the steady state of stochastic systems. A corollary are so-called thermodynamic uncertainty relations connecting precision of estimation to average dissipation. Here we consider this problem but for counting observables, i.e., trajectory observables which, in contrast to currents, are non-negative and nondecreasing in time (and possibly symmetric under time reversal). In the steady state, their fluctuations to all orders are bound from below by a Conway-Maxwell-Poisson distribution dependent only on the averages of the observable and of the dynamical activity. We show how to obtain the corresponding bounds for first-passage times (times when a certain value of the counting variable is first reached) and their uncertainty relations. Just like entropy production does for currents, dynamical activity controls the bounds on fluctuations of counting observables.

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Inequivalence of nonequilibrium path ensembles: the example of stochastic bridges

Cited by 38 publications

References 63 publications

Anomalous Scaling of Dynamical Large Deviations

Anomalous Scaling of Dynamical Large Deviations

First-passage dynamics of linear stochastic interface models: numerical simulations and entropic repulsion effect

Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables

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