Equivalence among different formalisms in the Tsallis entropy framework

Scarfone, Antonio Maria; Wada, Tatsuaki

doi:10.1016/j.physa.2007.05.029

Cited by 12 publications

(4 citation statements)

References 41 publications

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“…Following standard methods [11,24,32] a NFPE related to the STM-entropy (STM-NFPE) can be obtained starting from the continuity equation…”

Section: Nonlinear Fokker-planck Equationmentioning

confidence: 99%

Lie symmetries and related group-invariant solutions of a nonlinear Fokker-Planck equation based on the Sharma-Taneja-Mittal entropy

Scarfone¹,

Wada²

2009

Braz. J. Phys.

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In the framework of the statistical mechanics based on the Sharma-Taneja-Mittal entropy we derive a family of nonlinear Fokker-Planck equations characterized by the associated non-increasing Lyapunov functional. This class of equations describes kinetic processes in anomalous mediums where both super-diffusive and subdiffusive mechanisms arise contemporarily and competitively. We classify the Lie symmetries and derive the corresponding group-invariant solutions for the physically meaningful Uhlenbeck-Ornstein process. For the purely diffusive process we show that any localized state asymptotically approaches a bell shape well fitted by a generalized Gaussian which is, in general, a quasi-self-similar solution for this class of purely diffusive equations.

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“…Following standard methods [11,24,32] a NFPE related to the STM-entropy (STM-NFPE) can be obtained starting from the continuity equation…”

Section: Nonlinear Fokker-planck Equationmentioning

confidence: 99%

Lie symmetries and related group-invariant solutions of a nonlinear Fokker-Planck equation based on the Sharma-Taneja-Mittal entropy

Scarfone¹,

Wada²

2009

Braz. J. Phys.

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“…Such contributions can be associated, in particular, with non-extensive statistical mechanics. In the scientific literature, situations where diffusion contributions are written as a degree of probability density have been studied in most detail (see, for example, [21,24,[46][47][48][49][50][51][52][53][54]).…”

Section: Relationship Of the Fokker−plank−kolmogorov Equation Entropy Systemmentioning

confidence: 99%

On the construction of a family of anomalous-diffusion Fokker–Planck−Kolmogorov’s equations based on the Sharma–Taneja–Mittal entropy functional

Колесниченко

2021

MathMon

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A logical scheme for constructing thermodynamics of anomalous stochastic systems based on the nonextensive two-parameter (κ, ς) -entropy of Sharma–Taneja–Mittal (SHTM) is considered. Thermodynamics within the framework (2 - q) -statistics of Tsallis was constructed, which belongs to the STM family of statistics. The approach of linear nonequilibrium thermodynamics to the construction of a family of nonlinear equations of Fokker−Planck−Kolmogorov (FPK), is used, correlated with the entropy of the STM, in which the stationary solution of the diffusion equation coincides with the corresponding generalized Gibbs distribution obtained from the extremality (κ, ς) - entropy condition of a non-additive stochastic system. Taking into account the convexity property of the Bregman divergence, it was shown that the principle of maximum equilibrium entropy is valid for (κ, ς) - systems, and also was proved the H - theorem determining the direction of the time evolution of the non-equilibrium state of the system. This result is extended also to non-equilibrium systems that evolve to a stationary state in accordance with the nonlinear FPK equation. The method of the ansatz- approach for solving non-stationary FPK equations is considered, which allows us to find the time dependence of the probability density distribution function for non-equilibrium anomalous systems. Received diffusive equations FPК can be used, in particular, at the analysis of diffusion of every possible epidemics and pandemics. The obtained diffusion equations of the FPK can be used, in particular, in the analysis of the spread of various epidemics and pandemics.

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“…The case q < 1 has received much attention in the literature [12][13][14][15][16]. Stationary solutions for q < 1 correspond to power law distributions.…”

Section: Cutoff Distributionsmentioning

confidence: 99%

Nonextensive cutoff distributions of postural sway for the old and the young

Frank¹

2009

Physica A: Statistical Mechanics and its Applications

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Equivalence among different formalisms in the Tsallis entropy framework

Cited by 12 publications

References 41 publications

Lie symmetries and related group-invariant solutions of a nonlinear Fokker-Planck equation based on the Sharma-Taneja-Mittal entropy

Lie symmetries and related group-invariant solutions of a nonlinear Fokker-Planck equation based on the Sharma-Taneja-Mittal entropy

On the construction of a family of anomalous-diffusion Fokker–Planck−Kolmogorov’s equations based on the Sharma–Taneja–Mittal entropy functional

Nonextensive cutoff distributions of postural sway for the old and the young

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