Tsallis Entropy and the Transition to Scaling in Fragmentation

Sotolongo‐Costa, Oscar; Aguilar, Rodríguez; Rodgers, G. J.

doi:10.3390/e2040172

Cited by 30 publications

(19 citation statements)

References 6 publications

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“…The cluster size distribution reminds closely that of percolation at the critical point, where a lenght scale, or time scale, diverges leaving the system in a self-similar state [22]. More in general, it has been also suggested [23] that, optimizing Tsallis' entropy with natural constraints in a regime of long-range correlations, it is possible to derive a power-law hierarchical cluster size distribution which can be considered as paradigmatic of physical systems where multiscale interactions and geometric (fractal) properties play a key role in the relaxation behavior of the system. Therefore, we can say that the power-law scaling resulting in the distributions of Fig.2 strongly suggests a non-ergodic topology of a region of phase space in which the system remains trapped during the QSS regime (for the M1 i.c.…”

Section: Dynamical Frustration and Hierarchical Structurementioning

confidence: 99%

Metastability and Anomalous Behavior in the HMF Model: Connections to Nonextensive Thermodynamics and Glassy Dynamics

Pluchino

Rapisarda

Latora

2005

Complexity, Metastability and Nonextensivity

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We review some of the most recent results on the dynamics of the Hamiltonian Mean Field (HMF) model, a systems of N planar spins with ferromagnetic infiniterange interactions. We show, in particular, how some of the dynamical anomalies of the model can be interpreted and characterized in terms of the weak-ergodicity breaking proposed in frameworks of glassy systems. We also discuss the connections with the nonextensive thermodynamics proposed by Tsallis.

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Section: Dynamical Frustration and Hierarchical Structurementioning

confidence: 99%

Metastability and Anomalous Behavior in the HMF Model: Connections to Nonextensive Thermodynamics and Glassy Dynamics

Pluchino

Rapisarda

Latora

2005

Complexity, Metastability and Nonextensivity

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“…This distribution has been used successfully to account for the transition to scaling observed in the behavior of fragments in the process of breaking [9] as well as more subtle effects as the dimension cross-over between small and large fragment regions when thick clay plates and glass are fractured [12]. This is the cluster distribution we will use to discuss dipolar relaxation in self-similar structured systems.…”

Section: Cluster Size Distribution Functionmentioning

confidence: 99%

“…Following references [9], [12] we start from the expression of the generalized entropy proposed by Tsallis [5] and formulate the maximization process as in [13] …”

Section: Cluster Size Distribution Functionmentioning

confidence: 99%

“…Sotolongo et al [9] starting from Tsallis'expression have used the principle of maximum entropy with some natural constraints to derive a fragment size distribution function in a regime in which long-range correlations between all parts and scaling are present. This very general principle gives rise to scaling without additional assumptions and the resulting size distribution can be consider as a paradigm of physical systems where multiscale interactions play the key role in determining the hierarchical form of the fragment or cluster size distribution.…”

Section: Introductionmentioning

confidence: 99%

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Universal relaxation in nonextensive systems

Brouers

Sotolongo‐Costa

2003

Europhys. Lett.

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We have derived the dipolar relaxation function for a cluster model whose volume distribution was obtained from the generalized maximum Tsallis nonextensive entropy principle. The power law exponents of the relaxation function are simply related to a global fractal parameter α and for large time to the entropy nonextensivity parameter q. For intermediate times the relaxation follows a stretched exponential behavior. The asymptotic power law behaviors both in the time and the frequency domains coincide with those of the Weron generalized dielectric function derived from an extension of the Levy central limit theorem. They are in full agreement with the Jonscher universality principle. Moreover our model gives a physical interpretation of the mathematical parameters of the Weron stochastic theory and opens new paths to understand the ubiquity of self-similarity and power laws in the relaxation of large classes of materials in terms of their fractal and nonextensive properties.

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“…are highlighted in the works about "statistical seismology" by Vere-Jones [27][28][29]. In particular, entropy-based approaches to describe seismicity are used, for instance, in [30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Multifractal Dimensional Dependence Assessment Based on Tsallis Mutual Information

Angulo

Esquivel

2015

Entropy

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Entropy-based tools are commonly used to describe the dynamics of complex systems. In the last few decades, non-extensive statistics, based on Tsallis entropy, and multifractal techniques have shown to be useful to characterize long-range interaction and scaling behavior. In this paper, an approach based on generalized Tsallis dimensions is used for the formulation of mutual-information-related dependence coefficients in the multifractal domain. Different versions according to the normalizing factor, as well as to the inclusion of the non-extensivity correction term are considered and discussed. An application to the assessment of dimensional interaction in the structural dynamics of a seismic real series is carried out to illustrate the usefulness and comparative performance of the measures introduced.

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Tsallis Entropy and the Transition to Scaling in Fragmentation

Cited by 30 publications

References 6 publications

Metastability and Anomalous Behavior in the HMF Model: Connections to Nonextensive Thermodynamics and Glassy Dynamics

Metastability and Anomalous Behavior in the HMF Model: Connections to Nonextensive Thermodynamics and Glassy Dynamics

Universal relaxation in nonextensive systems

Multifractal Dimensional Dependence Assessment Based on Tsallis Mutual Information

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