Generalized-generalized entropies and limit distributions

Thurner, Stefan; Hanel, Rudolf

doi:10.1590/s0103-97332009000400011

Cited by 4 publications

(4 citation statements)

References 17 publications

(39 reference statements)

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“…The summary of results of his investigation is presented in Table 2. While the work of Wang (2008) deals with determination of entropy for a single variable case, Thurner and Hanel (2009) dealt with correlated Gaussian variables and found that the entropy of limiting distribution is non-Tsallis and they gave a generalized expression for entropy. Okionomou and Bagci (2017) showed, using classical calculus, that the MaxEnt distributions using Tsallis (2009) entropy and Renyi's entropy for specified constraints (information) are different.…”

Section: Information Theoretic Entropy and Mep: Brief Reviewmentioning

confidence: 99%

Shear capacity distribution of reinforced concrete beams: An information theoretic entropy approach

Yogalakshmi

Rao

2021

Advances in Structural Engineering

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Using the concept of information theoretic entropy, the probability density function (pdf) of shear capacity of the reinforced concrete beam with stirrup reinforcement is determined. Entropy, expressed in terms of Shannon functional, is maximized subjected to the statistical moment and normalization constraints of pdf of shear capacity. The statistical moments of shear capacity distribution are obtained using second-order approximation of shear capacity equation. The pdf so determined has strong statistical mechanics interpretation of maximum entropy principle. Also, a procedure for goodness-of-fit test has been proposed, for the given data, using the information theoretic entropy as a measure of goodness-of-fit. In the present investigation, beams of three different ranges of shear span to effective depth ratios are considered. The mechanics-based shear capacity equations, presented earlier by authors along with associated modelling errors, are used for estimating the statistical moments of shear capacity distribution. The computationally efficient approach of determination of maximum entropy distribution presented in this article can be viewed as an alternate to the process of determination of pdf using brute force Monte Carlo simulation approach.

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Section: Information Theoretic Entropy and Mep: Brief Reviewmentioning

confidence: 99%

Shear capacity distribution of reinforced concrete beams: An information theoretic entropy approach

Yogalakshmi

Rao

2021

Advances in Structural Engineering

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“…It is worthy to note that generalized trace-form entropies and the related distributions by means of a variational principleà la Jaynes have been discussed in [45,51,52]. In particular, [51,52] have derived the most general trace-form entropy compatible with the first three Khinchin axioms that result to be a sub-family of the most general class (9).…”

Section: Preliminarymentioning

confidence: 99%

“…In particular, [51,52] have derived the most general trace-form entropy compatible with the first three Khinchin axioms that result to be a sub-family of the most general class (9).…”

Section: Preliminarymentioning

confidence: 99%

Entropic Forms and Related Algebras

Scarfone

2013

Entropy

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Starting from a very general trace-form entropy, we introduce a pair of algebraic structures endowed by a generalized sum and a generalized product. These algebras form, respectively, two Abelian fields in the realm of the complex numbers isomorphic each other. We specify our results to several entropic forms related to distributions recurrently observed in social, economical, biological and physical systems including the stretched exponential, the power-law and the interpolating Bosons-Fermions distributions. Some potential applications in the study of complex systems are advanced.

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“…(25), in the cases δ = 2 and δ = 3, for which the equilibrium distributions were calculated exactly for a general φ(x) in the previous section [cf. Eqs.…”

Section: Normalization and Chemical Potential Analysismentioning

confidence: 99%

Probability distributions extremizing the nonadditive entropySδand stationary states of the corresponding nonlinear Fokker-Planck equation

2013

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Under the assumption that the physically appropriate entropy of generic complex systems satisfies thermodynamic extensivity, we investigate the recently introduced entropy S(δ) (which recovers the usual Boltzmann-Gibbs form for δ=1) and establish the microcanonical and canonical extremizing distributions. Using a generalized version of the H theorem, we find the nonlinear Fokker-Planck equation associated with that entropic functional and calculate the stationary-state probability distributions. We demonstrate that both approaches yield one and the same equation, which in turn uniquely determines the probability distribution. We show that the equilibrium distributions asymptotically behave like stretched exponentials, and that, in appropriate probability-energy variables, an interesting return occurs at δ=4/3. As a mathematically simple illustration, we consider the one-dimensional harmonic oscillator and calculate the generalized chemical potential for different values of δ.

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Generalized-generalized entropies and limit distributions

Cited by 4 publications

References 17 publications

Shear capacity distribution of reinforced concrete beams: An information theoretic entropy approach

Shear capacity distribution of reinforced concrete beams: An information theoretic entropy approach

Entropic Forms and Related Algebras

Probability distributions extremizing the nonadditive entropySδand stationary states of the corresponding nonlinear Fokker-Planck equation

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