Convoluted Gauss-Levy distributions and exploding Coulomb clusters

Ébeling, W.; Romanovsky, M. Yu.; Sokolov, Igor M.; Valuev, Ilya

doi:10.1140/epjst/e2010-01280-5

Cited by 10 publications

(18 citation statements)

References 35 publications

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“…Divergent moments of Lévy statistics and Lévy motion seem to stay in conflict with energetic and thermodynamics of the stochastic differential equation of the Langevin type 23,44,57,58 . Yet, accumulating evidence shows that Markovian Lévy flights (LFs) with distribution of jumps emerging from the generalized version of the central limit theorem are well suited representations of complex phenomena, to name just a few recent applications of LFs in description of mental searches 61 , analysis of free neutron output in a fusion experiment with a deuteron plasma 56 , investigations of generegulatory networks 62 or examination of self-regulatory motion of insects 63 .…”

Section: Discussionmentioning

confidence: 99%

Peculiarities of escape kinetics in the presence of athermal noises

Capała

Dybiec

Gudowska–Nowak

2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Stochastic evolution of various reaction networks is commonly described in terms of noise assisted escape of an overdamped particle from a potential well, as devised by the paradigmatic Langevin equation. When implemented for systems close to equilibrium, the approach correctly explains emergence of Boltzmann distribution for the ensemble of trajectories generated by Langevin equation and relates intensity of the noise strength to the mobility. This scenario can be further generalized to include effects of non-thermal, external burst-like forcing modeled by Lévy noise. In the paper forward and reverse kinetics of Langevin equations with Lévy noise are analyzed for simple model of potential wells pointing to the most probable escape which is executed via a single long jump. Heavy tails of Lévy noise distributions not only facilitate escape kinetics, but more importantly, change the escape protocol by altering final stationary state to a non-Boltzmann, non-equilibrium form. As a result, contrary to the kinetics induced by a Gaussian white noise, escape rates in environments with Lévy noise are determined not by the barrier height, but instead, by the barrier width. We discuss consequences of simultaneous action of thermal and Lévy noises on statistics of passage times and population of reactants in double-well potentials.

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Section: Discussionmentioning

confidence: 99%

Peculiarities of escape kinetics in the presence of athermal noises

Capała

Dybiec

Gudowska–Nowak

2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…Among various problems addressed in the field of Lévy-noise driven dynamics is the origin of superdiffusive transport in momentum space investigated in a number of studies [8][9][10][11]. In particular, based on the Langevin model with linear friction proportional to velocity and non-Gaussian noise, superdiffusive transport in velocity space for a magnetized plasma has been analyzed [8].…”

Section: Introductionmentioning

confidence: 99%

Heat and work distributions for mixed Gauss–Cauchy process

Kuśmierz¹,

Rubı́²,

Gudowska–Nowak³

2014

J. Stat. Mech.

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Abstract. We analyze energetics of a non-Gaussian process described by a stochastic differential equation of the Langevin type. The process represents a paradigmatic model of a nonequilibrium system subject to thermal fluctuations and additional external noise, with both sources of perturbations considered as additive and statistically independent forcings. We define thermodynamic quantities for trajectories of the process and analyze contributions to mechanical work and heat. As a working example we consider a particle subjected to a drag force and two statistically independent Lévy white noises with stability indices α = 2 and α = 1. The fluctuations of dissipated energy (heat) and distribution of work performed by the force acting on the system are addressed by examining contributions of Cauchy fluctuations (α = 1) to either bath or external force acting on the system.

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“…Since the Langevin Equation (25) is linear, its solution depends linearly on two statistically independent noises and the corresponding probability distribution function (p(x, t)) of the dynamic variable (x(t)) attains the convoluted form of two Lévy PDFs with the stability indices α = 1 and α = 2. The corresponding characteristic function is expressed by a product p(k, t) = e ikµ(t)−σ 2 (t)|k| 2 −γ(t)|k| , (26) and fulfills [56,70,71] the generalized Smoluchowski-Fokker-Planck equation…”

Section: Linear Response and Fluctuation-dissipation Relationship Undmentioning

confidence: 99%

Thermodynamics of Superdiffusion Generated by Lévy–Wiener Fluctuating Forces

Kuśmierz

Dybiec

Gudowska–Nowak

2018

Entropy

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Scale free Lévy motion is a generalized analogue of the Wiener process. Its time derivative extends the notion of “white noise” to non-Gaussian noise sources, and as such, it has been widely used to model natural signal variations described by an overdamped Langevin stochastic differential equation. Here, we consider the dynamics of an archetypal model: a Brownian-like particle is driven by external forces, and noise is represented by uncorrelated Lévy fluctuations. An unperturbed system of that form eventually attains a steady state which is uniquely determined by the set of parameter values. We show that the analyzed Markov process with the stability index α < 2 violates the detailed balance, i.e., its stationary state is quantified by a stationary probability density and nonvanishing current. We discuss consequences of the non-Gibbsian character of the stationary state of the system and its impact on the general form of the fluctuation–dissipation theorem derived for weak external forcing.

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Convoluted Gauss-Levy distributions and exploding Coulomb clusters

Cited by 10 publications

References 35 publications

Peculiarities of escape kinetics in the presence of athermal noises

Peculiarities of escape kinetics in the presence of athermal noises

Heat and work distributions for mixed Gauss–Cauchy process

Thermodynamics of Superdiffusion Generated by Lévy–Wiener Fluctuating Forces

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