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Tsallis distribution
About: Tsallis distribution is a research topic. Over the lifetime, 304 publications have been published within this topic receiving 14331 citations.
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TL;DR: In this paper, a generalized form of entropy was proposed for the Boltzmann-Gibbs statistics with the q→1 limit, and the main properties associated with this entropy were established, particularly those corresponding to the microcanonical and canonical ensembles.
Abstract: With the use of a quantity normally scaled in multifractals, a generalized form is postulated for entropy, namelyS
q
≡k [1 – ∑
i=1
W
p
i
q
]/(q-1), whereq∈ℝ characterizes the generalization andp
i are the probabilities associated withW (microscopic) configurations (W∈ℕ). The main properties associated with this entropy are established, particularly those corresponding to the microcanonical and canonical ensembles. The Boltzmann-Gibbs statistics is recovered as theq→1 limit.
8,239 citations
TL;DR: The nonextensivity parameter q occurring in some of the applications of Tsallis statistics is shown to be given, in the q>1 case, entirely by the fluctuations of the parameters of the usual exponential distribution.
Abstract: The nonextensivity parameter $q$ occurring in some of the applications of Tsallis statistics (known also as index of the corresponding L\'evy distribution) is shown to be given, in the $qg1$ case, entirely by the fluctuations of the parameters of the usual exponential distribution.
620 citations
TL;DR: Anomalous diffusion and non-Gaussian statistics are detected experimentally in a two-dimensional driven-dissipative system and the probability distribution function fits a Tsallis distribution, yielding q, a measure of nonextensivity for non- Gaussian statistics.
Abstract: Anomalous diffusion and non-Gaussian statistics are detected experimentally in a two-dimensional driven-dissipative system A single-layer dusty plasma suspension with a Yukawa interaction and frictional dissipation is heated with laser radiation pressure to yield a structure with liquid ordering Analyzing the time series for mean-square displacement, superdiffusion is detected at a low but statistically significant level over a wide range of temperatures The probability distribution function fits a Tsallis distribution, yielding q, a measure of nonextensivity for non-Gaussian statistics
319 citations
TL;DR: It is demonstrated experimentally that the momentum distribution of cold atoms in dissipative optical lattices is a Tsallis distribution, which can be continuously varied by changing the parameters of the optical potential.
Abstract: We demonstrated experimentally that the momentum distribution of cold atoms in dissipative optical lattices is a Tsallis distribution. The parameters of the distribution can be continuously varied by changing the parameters of the optical potential. In particular, by changing the depth of the optical lattice, it is possible to change the momentum distribution from Gaussian, at deep potentials, to a power-law tail distribution at shallow optical potentials.
286 citations
TL;DR: In this paper, an improved form is proposed for describing the transverse momentum distribution and fits are presented together with estimates of the parameter q and the temperature T for relativistic high-energy quantum distributions.
Abstract: Transverse momentum distributions measured by the STAR and PHENIX Collaborations at the Relativistic Heavy Ion Collider and by the ALICE, ATLAS and CMS Collaborations at the Large Hadron Collider can be considered in the framework of relativistic thermodynamics using the Tsallis distribution. Theoretical issues are clarified concerning the thermodynamic consistency in the case of relativistic high-energy quantum distributions. An improved form is proposed for describing the transverse momentum distribution and fits are presented together with estimates of the parameter q and the temperature T .
248 citations