Generalised cascades

Queirós, Sı́lvio M. Duarte

doi:10.1590/s0103-97332009000400019

Cited by 4 publications

(3 citation statements)

References 13 publications

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“…(1) has been employed in a growing number of theoretical and empirical works on a large variety of themes. Examples include scale-free networks [10][11][12][13][14], dynamical systems [15][16][17][18][19][20][21][22][23][24][25][26][27], algebraic structures [28][29][30][31] among other topics in statistical physcics [32][33][34][35][36].…”

Section: Q-exponential Distributionmentioning

confidence: 99%

See 1 more Smart Citation

q-distributions in complex systems: a brief review

Picoli¹,

Mendes²,

Malacarne³

et al. 2009

Braz. J. Phys.

103

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The nonextensive statistical mechanics proposed by Tsallis is today an intense and growing research field. Probability distributions which emerges from the nonextensive formalism (q-distributions) have been applied to an impressive variety of problems. In particular, the role of q-distributions in the interdisciplinary field of complex systems has been expanding. Here, we make a brief review of q-exponential, q-Gaussian and q-Weibull distributions focusing some of their basic properties and recent applications. The richness of systems analyzed may indicate future directions in this field.

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Section: Q-exponential Distributionmentioning

confidence: 99%

“…For instance, q-Gaussian arises from the non-linear diffusion (porous media) equation [84] and from a generalization of the central limit theorem [3]. Another example is the q-lognormal distribution which emerges from generalized cascades [28].…”

Section: Basis For Q-distributionsmentioning

confidence: 99%

q-distributions in complex systems: a brief review

Picoli¹,

Mendes²,

Malacarne³

et al. 2009

Braz. J. Phys.

103

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“…In [40], the authors investigate the possibility to generate random variables, by using the q-product. If q < 3 2 , the Lyapunov's Central Limit Theorem can be applied.…”

Section: The Valuementioning

confidence: 99%

Entropy- A Tale of Ice and Fire

Hirica¹,

Pripoae²,

Pripoae³

et al. 2023

Annals of West University of Timisoara - Mathematics and Computer Science

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In this review paper, we recall, in a unifying manner, our recent results concerning the Lie symmetries of nonlinear Fokker-Plank equations, associated to the (weighted) Tsallis and Kaniadakis entropies. The special values of the Tsallis parameters, highlighted by the classification of these symmetries, clearly indicate algebraic and geometric invariants which differentiate the Lie algebras involved. We compare these values with the ones previously obtained by several authors, and we try to establish connections between our theoretical families of entropies and specific entropies arising in several applications found in the literature. We focus on the discovered correlations, but we do not neglect dissimilarities, which might provide -in the future-deeper details for an improved extended panorama of the Tsallis entropies.

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