q-distributions in complex systems: a brief review

Picoli, S.; Mendes, R. S.; Malacarne, L. C.; Paupitz, Ricardo

doi:10.1590/s0103-97332009000400023

Cited by 103 publications

(88 citation statements)

References 125 publications

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“…q = 1/(2 − q) and B q = (2 − q)/B q (Picoli et al, 2009). The cumulative distribution P (> τ ) also exhibits the qexponential form as the physical probability p(τ ).…”

Section: Interevent Time Distributionmentioning

confidence: 99%

Non-extensivity and long-range correlations in the earthquake activity at the West Corinth rift (Greece)

Michas

Vallianatos

Sammonds

2013

Nonlin. Processes Geophys.

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Abstract. In the present work the statistical properties of the earthquake activity in a highly seismic region, the West Corinth rift (Central Greece), are being studied by means of generalized statistical physics. By using a dataset that covers the period 2001-2008, we investigate the earthquake energy distribution and the distribution of the time intervals (interevent times) between the successive events. As has been reported previously, these distributions exhibit complex statistical properties and fractality. By using detrended fluctuation analysis (DFA), a well-established method for detection of long-range correlations in non-stationary signals, it is shown that long-range correlations are also present in the earthquake activity. The existence of these properties motivates us to use non-extensive statistical physics (NESP) to investigate the statistical properties of the frequencymagnitude and the interevent time distributions, along with other well-known relations in seismology, such as the gamma distribution for interevent times. The results of the analysis indicate that the statistical properties of the earthquake activity can be successfully reproduced by means of NESP and that the earthquake activity at the West Corinth rift is correlated at all-time scales.

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“…q = 1/(2 − q) and B q = (2 − q)/B q (Picoli et al, 2009). The cumulative distribution P (> τ ) also exhibits the qexponential form as the physical probability p(τ ).…”

Section: Interevent Time Distributionmentioning

confidence: 99%

Non-extensivity and long-range correlations in the earthquake activity at the West Corinth rift (Greece)

Michas

Vallianatos

Sammonds

2013

Nonlin. Processes Geophys.

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“…Approximating the number of microstates as (19) we obtain that the probability of the microstate of the system S is proportional to the Boltzmann factor…”

Section: Canonical Ensemble In Boltzmann-gibbs Statistical Mechanicsmentioning

confidence: 99%

“…The non-extensive statistical mechanics has been used to describe phenomena in various in high-energy physics [4], spin-glasses [5], cold atoms in optical lattices [6], trapped ions [7], anomalous diffusion [8,9], dusty plasmas [10], low-dimensional dissipative and conservative maps in the dynamical systems [11][12][13], turbulent flows [14], Langevin dynamics with fluctuating temperature [15,16]. Concepts related to the non-extensive statistical mechanics have found applications not only in physics but in chemistry, biology, mathematics, economics, and informatics as well [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Canonical ensemble in non-extensive statistical mechanics

Ruseckas

2016

Physica A: Statistical Mechanics and its Applications

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The framework of non-extensive statistical mechanics, proposed by Tsallis, has been used to describe a variety of systems. The non-extensive statistical mechanics is usually introduced in a formal way, using the maximization of entropy. In this article we investigate the canonical ensemble in the non-extensive statistical mechanics using a more traditional way, by considering a small system interacting with a large reservoir via short-range forces. The reservoir is characterized by generalized entropy instead of the Boltzmann-Gibbs entropy. Assuming equal probabilities for all available microstates we derive the equations of the non-extensive statistical mechanics. Such a procedure can provide deeper insight into applicability of the non-extensive statistics.

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“…One may mention, for instance, high-energy physics [3]- [4], spin-glasses [5], cold atoms in optical lattices [6], trapped ions [7], anomalous diffusion [8], [9], dusty plasmas [10], low-dimensional dissipative and conservative maps in dynamical systems [11], [12], [13], turbulent flows [14], Levy flights [15], the QCD-based Nambu, Jona, Lasinio model of a many-body field theory [16], etc. Notions related to qstatistical mechanics have been found useful not only in physics but also in chemistry, biology, mathematics, economics, and informatics [17], [18], [19].…”

Section: Introductionmentioning

confidence: 99%

On the putative essential discreteness of q-generalized entropies

Plastino

Rocca

2017

Physica A: Statistical Mechanics and its Applications

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It has been argued in [EPL 90 (2010) 50004], entitled Essential discreteness in generalized thermostatistics with non-logarithmic entropy, that "continuous Hamiltonian systems with long-range interactions and the so-called q-Gaussian momentum distributions are seen to be outside the scope of non-extensive statistical mechanics". The arguments are clever and appealing. We show here that, however, some mathematical subtleties render them unconvincing

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q-distributions in complex systems: a brief review

Cited by 103 publications

References 125 publications

Non-extensivity and long-range correlations in the earthquake activity at the West Corinth rift (Greece)

Non-extensivity and long-range correlations in the earthquake activity at the West Corinth rift (Greece)

Canonical ensemble in non-extensive statistical mechanics

On the putative essential discreteness of q-generalized entropies

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