Emergence of Tsallis statistics as a consequence of invariance

Davis, Sergio; Gutiérrez, Gonzalo

doi:10.1016/j.physa.2019.122031

Cited by 10 publications

(5 citation statements)

References 20 publications

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“…This is consistent with the derivation in Ref. [17] that produces the q-canonical ensemble from invariance requirements on the fundamental inverse temperature β F (E), and in both cases the parameters q and β 0 are not fixed a priori.…”

Section: Discussionsupporting

confidence: 91%

“…In the case of superstatistics, we can show a connection between the moments of P (β|E, S) and β F . First, we use equations ( 28) and (17) as…”

Section: The Fundamental Inverse Temperaturementioning

confidence: 99%

“…This equality gives meaning to the fundamental inverse temperature in superstatistics [17], as the conditional mean inverse temperature for a fixed energy E.…”

Section: The Fundamental Inverse Temperaturementioning

confidence: 99%

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The $q$-canonical ensemble as a consequence of Bayesian superstatistics

Davis¹

2021

Preprint

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In this work it is shown that the main ensemble of Tsallis nonextensive statistics, namely the χ 2 -superstatistics, can be obtained as a noninformative prior distribution that is singled out by the mathematical structure of superstatistics itself. There are no assumptions involved about the physics of the systems of interest, or regarding their complexity or range of interactions, which supports the thesis that the success of the χ 2 -superstatistics is information-theoretical in its origin, and explainable in terms of Jaynes' original maximum entropy principle.

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Section: Discussionsupporting

confidence: 91%

“…In the case of superstatistics, we can show a connection between the moments of P (β|E, S) and β F . First, we use equations ( 28) and (17) as…”

Section: The Fundamental Inverse Temperaturementioning

confidence: 99%

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The $q$-canonical ensemble as a consequence of Bayesian superstatistics

Davis¹

2021

Preprint

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“…That is, in this case the temperature function matches the fundamental temperature [22] of the whole (system plus environment), evaluated at the energy of the environment. This is precisely the result recently shown in Ref.…”

Section: A Microscopic Definition Of Temperaturementioning

confidence: 92%

On the possible distributions of temperature in nonequilibrium steady states

Davis

2020

J. Phys. A: Math. Theor.

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Superstatistics is a framework in nonequilibrium statistical mechanics that successfully describes a wide variety of complex systems, including hydrodynamic turbulence, weakly-collisional plasmas, cosmic rays, power grid fluctuations, among several others. In this work we analyze the class of nonequilibrium steady-state systems consisting of a subsystem and its environment, and where the subsystem is described by the superstatistical framework. In this case we provide an answer to the mechanism by which a broad distribution of temperature arises, namely due to correlation between subsystem and environment. We prove that there is a unique microscopic definition B of inverse temperature compatible with superstatistics, in the sense that all moments of B and β = 1/(kBT ) coincide. The function B however, cannot depend on the degrees of freedom of the system itself, only on the environment, in full agreement with our previous impossibility theorem [Physica A 505, 864-870 (2018)]. The present results also constrain the possible joint ensembles of system and environment compatible with superstatistics.

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“…The second term in the left expectation corresponds to the microcanonical inverse temperature β Ω (Eq. 13), while the first term is the so-called fundamental inverse temperature [18]…”

Section: The Conjugate Variables Theoremmentioning

confidence: 99%

Fluctuation theorems in nonextensive statistics

Umpierrez¹,

Davis²

2019

Preprint

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Nonextensive statistics is a formalism of statistical mechanics that describes the ocurrence of power-law distributions in complex systems, particularly the so-called q-exponential family of distributions. In this work we present the use of fluctuation theorems for q-canonical ensembles as a powerful tool to readily obtain statistical properties. In particular, we have obtained strong conditions for the possible values of q depending on the density of states of the system.

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Emergence of Tsallis statistics as a consequence of invariance

Cited by 10 publications

References 20 publications

The $q$-canonical ensemble as a consequence of Bayesian superstatistics

The $q$-canonical ensemble as a consequence of Bayesian superstatistics

On the possible distributions of temperature in nonequilibrium steady states

Fluctuation theorems in nonextensive statistics

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