Incomplete statistics: nonextensive generalizations of statistical mechanics

Wang, Qiuping A.

doi:10.1016/s0960-0779(00)00113-2

Cited by 85 publications

(115 citation statements)

References 10 publications

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“…In what follows, we will try to give the general expression of the correlation energy in ISM because this relation is implicit in Tsallis' scenario [15]. The following discussion is for 0 < q < ∞, the permitted interval of q value in ISM [2].…”

Section: Factorization Of the Joint Probabilitymentioning

confidence: 99%

“…In this section, we will discuss an application of the so called Incomplete Statistical Mechanics (ISM) [2], a new version of the nonextensive statistical mechanics (NSM) based on the normalization condition i p q i = 1 where q is a positive parameter. q = 1 corresponds to the fact that the probability distributions {p i } with incomplete random variables [5] do not sum to one.…”

Section: Re-establishment Of the Zeroth Law Of Thermodynamicsmentioning

confidence: 99%

“…plays a decisive role for the success of the generalized statistical mechanics [1,2] because it is capable of reproducing unusual distributions of non gaussian type which are met frequently in nature (see reference [1] and the references therein). Very recently, distribution functions of type Eq.…”

Section: Introductionmentioning

confidence: 99%

“…with β = Z 1−q kT in Wang's incomplete statistics scenario [2] devoted to describe inexact or incomplete probability distribution [5] due to neglected interactions in the system hamiltonian. It is noteworthy that Eq.…”

Section: Introductionmentioning

confidence: 99%

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Nonextensive distribution and factorization of the joint probability

Wang

Pezeril

Nivanen

et al. 2002

Chaos, Solitons & Fractals

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The problem of factorization of a nonextensive probability distribution is discussed. It is shown that the correlation energy between the correlated subsystems in the canonical composite system can not be neglected even in the thermodynamic limit. In consequence, the factorization approximation should be employed carefully according to different systems. It is also shown that the zeroth law of thermodynamics can be established within the framework of the Incomplete Statistical Mechanics (ISM ).

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Section: Factorization Of the Joint Probabilitymentioning

confidence: 99%

Section: Re-establishment Of the Zeroth Law Of Thermodynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nonextensive distribution and factorization of the joint probability

Wang

Pezeril

Nivanen

et al. 2002

Chaos, Solitons & Fractals

Self Cite

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show abstract

“…Nevertheless, there are instances where the states of a physical system are complicated by either incomplete statistics [1], fluctuations in the statistical parameters defining the system [2][3][4], long-range correlations [5][6][7] or the nonlinear dynamics of the system [8]. In each of these cases models have been defined which lead to an escort probability, which modifies the probabilities by a power-law, a non-additive entropy function, and a generalization of the Gaussian distribution, known as the q-Gaussian [9,10].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear statistical coupling

Nelson

Umarov

2010

Physica A: Statistical Mechanics and its Applications

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-By considering a nonlinear combination of the probabilities of a system, a physical interpretation of Tsallis statistics as representing the nonlinear coupling or decoupling of statistical states is proposed. The escort probability is interpreted as the coupled probability, with Gaussian distributions. This conjugate relationship has been used to extend the generalized Fourier transform to the compact-support domain and to define a scale-invariant correlation structure with heavy-tail limit distribution. In the present paper, we show that the conjugate is a mapping between the source of nonlinearity in non-stationary stochastic processes and the nonlinear coupling which defines the coupled-Gaussian limit distribution. The effects of additive and multiplicative noise are shown to be separable into the coupled-variance and the coupling parameter Q, providing further evidence of the importance of the generalized moments.

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Thermodynamics of action and organization in a system

Chatterjee

2015

Complexity

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Complexity in nature is astounding yet the explanation lies in the fundamental laws of physics. The Second Law of Thermodynamics and the Principle of Least Action are the two theories of science that have always stood the test of time. In this article, we use these fundamental principles as tools to understand how and why things happen. In order to achieve that, it is of absolute necessity to define things precisely yet preserving their applicability in a broader sense. We try to develop precise, mathematically rigorous definitions of the commonly used terms in this context, such as action, organization, system, process, etc., and in parallel argue the behavior of the system from the first principles. This article, thus, acts as a mathematical framework for more discipline‐specific theories. © 2015 Wiley Periodicals, Inc. Complexity 21: 307–317, 2016

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Incomplete statistics: nonextensive generalizations of statistical mechanics

Cited by 85 publications

References 10 publications

Nonextensive distribution and factorization of the joint probability

Nonextensive distribution and factorization of the joint probability

Nonlinear statistical coupling

Thermodynamics of action and organization in a system

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