Untitled

2009

Russ Phys J

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536.75The Abel entropy group and its matrix representation with the general law of nonextensive entropy composition and quadratic nonlinearity are defined. Four types of matrices for the corresponding parametrical entropies are given and geometries for their measures are determined. New two-parameter entropy is introduced, and a distribution is found for equilibrium thermodynamics of nonextensive systems.

Section: Institute Of Mechanics Andmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An entropy group and its representation in thermodynamics of nonextensive systems

2009

Russ Phys J

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“…(14) and, accordingly, condition (13) need not be fulfilled in the general case. Then, inequality (16) does not hold and one cannot argue that a given process of generation is self-organizing.…”

mentioning

confidence: 99%

“…families, which is inconsistent with the approach used in [14,15]. That only such an averaging procedure over unnormalized distributions of q p is valid [8,9] also follows from the condition of thermodynamic equilibrium for nonextensive systems [16].…”

mentioning

confidence: 99%

I-theorem and self-organization in the van der Pol generator

2012

J. Phys.: Conf. Ser.

Abstract. Based on the S-and I-theorems of evolution of q-entropy and q-discrimination information, the process of self-organization developing in the van der Pol generator with variation of the feedback parameter at induced transitions between stationary states in an open nonextensive system is studied.To date, many properties of nonextensive (nonadditive) statistical systems that are described by nonGaussian and non-Gibbs distributions in various fields of physics have been studied. A new area of research -nonextensive statistical mechanics and thermodynamics -is being developed. A detailed review of related works is given in [1][2][3].For additive systems, self-organization in the generator was considered in [4], where the S-theorem on decrease in the renormalized Boltzmann-Gibbs-Shannon entropy (this entropy corresponds to the equal values of the average energy) was formulated for the first time. The I-theorem states that the renormalized Kullback discrimination information increases during self-organization of open systems [5,6].The van der Pol generator is described by the Langevin equations Its solution for a stationary state with given noise ( )

Evolution of the difference information in the process of the Fermi and Bose gas self-organization for nonextensive systems

2009

Russ Phys J

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A theoretical-informational description of transitions between stationary states in the control parameter space is given for quantum nonextensive self-organized systems. A new measure of the difference information is given, and the S-and I-theorems on changes of parameterized quantum entropy and difference information measures are proved under the Gibbs condition for the Hamilton effective function.