Superstatistics from a dynamical perspective: Entropy and relaxation

Ourabah, Kamel

doi:10.1103/physreve.109.014127

Cited by 3 publications

(1 citation statement)

References 110 publications

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“…There are several possibilities when attempting to define an entropy for a superstatistical system, as we must be careful of precisely agreeing on the set of degrees of freedom we are describing. Previous and recent works discussing the concept of entropy in the context of superstatistics give further insight on this issue [46][47][48].…”

Section: A Superstatistical Distance From Canonical Equilibriummentioning

confidence: 98%

A superstatistical measure of distance from canonical equilibrium

Davis

2024

J. Phys. A: Math. Theor.

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Non-equilibrium systems in steady states are commonly described by generalized statistical mechanical frameworks such as superstatistics, which assumes that the inverse temperature β = 1 / ( k B T ) is an unknown quantity having some pre-established statistical distribution. The uncertainty in β is usually understood as the fluctuation of a physical observable, however, it has been previously proved (Davis and Gutiérrez 2018 Physica A 505 864–70) that β in a superstatistical model cannot be associated to an observable function B ( Γ ) of the microstates Γ. In this work, we provide an information-theoretical interpretation of this theorem by introducing a new quantity D , the mutual information between β and Γ. Our results show that D is also a measure of departure from canonical equilibrium, and reveal a minimum, non-zero uncertainty about β given Γ for every non-canonical superstatistical ensemble. The behavior of D is illustrated in the case of a collisionless plasma described by kappa distributions, revealing the precise sense in which the spectral index κ can be understood as a measure of distance from equilibrium.

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Section: A Superstatistical Distance From Canonical Equilibriummentioning

confidence: 98%

A superstatistical measure of distance from canonical equilibrium

Davis

2024

J. Phys. A: Math. Theor.

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Bounded diffusing diffusivities: Brownian yet non-Gaussian diffusion

Luo,

Du,

Guo

et al. 2024

Phys. Scr.

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Brownian yet non-Gaussian diﬀusion has been recently reported in a huge number of biological and soft matter systems. Meanwhile, an archetypal theoretical model called “diﬀusing diﬀusivities” is proposed to interpret it. Based on this spirit of diﬀusing diﬀusivities, we extend the original diﬀusing diﬀusivities (with the unbounded exponential distribution) to the case that the diﬀusivity is constructed by a bounded stochastic process, i.e., corresponding diﬀusivities (with certain upper and lower bounds) obeying bounded power-law distribution. We demonstrate that Brownian yet non-Gaussian diﬀusion can be reproduced by this bounded diﬀusing diﬀusivities, via numerical simulations and analytic derivations. Speciﬁcally, the short-time distribution of displacement, as the indicator of the Brownian yet non-Gaussian diﬀusion, is derived analytically by means of superstatistical approach. This short-time distribution is distinct from the Laplace distribution that appears in the original model. The long-time Gaussian displacement distribution is obtained by utilizing the subordination concept. The bounded diﬀusing diﬀusivity here may be beneﬁcial to further understanding the diﬀusive process of particles in complex and inhomogeneous environments. Our work enriches the diﬀusing diﬀusivity family and sheds new light on the concept of the Brownian yet non-Gaussian diﬀusion under stochastic process.

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Kappa-tail Technique: Modeling and Application to Solar Energetic Particles Observed by Parker Solar Probe

Livadiotis,

Cummings,

Cuesta

et al. 2024

ApJ

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We develop the kappa-tail fitting technique, which analyzes observations of power-law tails of distributions and energy flux spectra, and connects them to theoretical modeling of kappa distributions, to determine the thermodynamics of the examined space plasma. In particular, we (i) construct the associated mathematical formulation; (ii) prove its decisive lead for determining whether the observed power-law is associated with kappa distributions; and (iii) provide a validation of the technique using pseudo-observations of typical input plasma parameters. Then, we apply this technique to a case study by determining the thermodynamics of solar energetic particle (SEP) protons, for an SEP event observed on 2021 April 17, by the Parker Solar Probe (PSP)/Integrated Science Investigation of the Sun instrument suite on board PSP. The results show SEP temperatures and densities of the order of ∼1 MeV and ∼5 × 10−7 cm−3, respectively.

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Superstatistics from a dynamical perspective: Entropy and relaxation

Cited by 3 publications

References 110 publications

A superstatistical measure of distance from canonical equilibrium

A superstatistical measure of distance from canonical equilibrium

Bounded diffusing diffusivities: Brownian yet non-Gaussian diffusion

Kappa-tail Technique: Modeling and Application to Solar Energetic Particles Observed by Parker Solar Probe

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