Nonextensive statistical mechanics: Applications to high energy physics

Tsallis, Constantino

doi:10.1051/epjconf/20111305001

Cited by 7 publications

(6 citation statements)

References 60 publications

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“…Results obtained for the Alps revealed that the frequency distribution of the modelled failure volumes obeys a power-law with a scaling exponent in the range of the known empirical values (Brunetti et al, 2009a), and exhibits a distinct "rollover" for small size failures. Chen et al (2011) proposed an alternative way for describing the scaling properties of landslide sizes exploiting non-extensive statistical mechanics, or Tsallis statistics (Tsallis, 1988(Tsallis, , 1999(Tsallis, , 2011, a formal extension of the Boltzmann-Gibbs statistics. This approach relies on the postulate that a system composed by two independent statistical systems has an entropy given by the entropies of the two subsystems plus a correction term dependent on a parameter that controls the degree of non-additivity.…”

Section: Comparison With Other Modeling Approachesmentioning

confidence: 99%

Scaling properties of rainfall induced landslides predicted by a physically based model

2014

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Natural landslides exhibit scaling properties revealed by power law relationships. These relationships include the frequency of the size (e.g., area, volume) of the landslides, and the rainfall conditions responsible for slope failures in a region. Reasons for the scaling behavior of landslides are poorly known. We investigate the possibility of using the Transient Rainfall Infiltration and Grid-Based Regional Slope-Stability analysis code (TRIGRS), a consolidated, physically-based, numerical model that describes the stability/instability conditions of natural slopes forced by rainfall, to determine the frequency statistics of the area of the unstable slopes and the rainfall intensity (I) -duration (D) conditions that result in landslides in a region. We apply TRIGRS in a portion of the Upper Tiber River Basin, Central Italy. The spatially distributed model predicts the stability/instability conditions of individual grid cells, given the local terrain and rainfall conditions. We run TRIGRS using multiple, synthetic rainfall histories, and we compare the modeling results with empirical evidences of the area of landslides and of the rainfall conditions that have caused landslides in the study area. Our findings revealed that TRIGRS is capable of reproducing the frequency of the size of the patches of terrain predicted as unstable by the model, which match the frequency size statistics of landslides in the study area, and the mean rainfall D, I conditions that result in unstable slopes in the study area, which match rainfall I-D thresholds for possible landslide occurrence. Our results are a step towards understanding the mechanisms that give rise to landslide scaling properties.

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Section: Comparison With Other Modeling Approachesmentioning

confidence: 99%

Scaling properties of rainfall induced landslides predicted by a physically based model

2014

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“…[74]. For more details about the non-extensive statistics application in various fields in physics , cosmology and astronomy see [54,[75][76][77][78][79].…”

Section: Essential Features Of Non-extensive Statisticsmentioning

confidence: 99%

The Magnetic Field Effect on Thermodynamics of Hot QCD Matter using Extensive and non-Extensive Statistics

Tarek¹,

Ahmed²,

Shalaby³

2021

Preprint

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We study in detail the thermodynamics of the quantum chromodynamics (QCD) matter utilizing two different statistics, extensive and non-extensive. The thermodynamics such as (pressure, number density, energy density , entropy and magnetization) are determined from both statistics at zero and non-zero magnetic field, eB = 0, 0.2, 0.3 GeV 2 . The magnetic field effect appears by adding a vacuum contribution to the free energy along side the thermal contribution. The extensive thermodynamics can be emerged from the resonance hadron gas model which is incorporated in the present work. Accordingly, we repeat our calculations at zero and non-zero magnetic field for the non-extensive statistics. The theoretical results of thermodynamical quantities calculated from both statistics are confronted to the lattice results which show a reasonable agreement with the extensive thermodynamics, but overrated in non-extensive thermodynamics at high temperature only and higher entropic index. The response of the QCD matter due to the magnetic field is additionally examined, and it is concluded that QCD matter is considered as a paramagnetic matter.

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“…Complex systems are not used only in the domain of physics but also in other domains like biology, economics, and so on [11]. For more details about the non-extensive statistics application in various fields in physics and astronomy see References [5,[12][13][14][15][16]. Specifically, many systems deviate from the BG statistics, and it was necessary to generalize the original ones.…”

Section: Introduction Historical Review and Introductory Remarksmentioning

confidence: 99%

Non-Extensive Thermodynamics Effects in the Cosmology of f(T) Gravity

2021

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Using f(T) gravitational theory, we construct modified cosmological models via the first law of thermodynamics by using the non-extensive thermodynamics framework, the effects of which are captured by the parameter δ. The resulting cosmological equations are modified compared to the standard Einstein-Hilbert ones, with the modifications coming from the f(T) gravitational theory and from the non-extensive parameter which quantifies the non-extensive thermodynamics effects quantified by the parameter δ, which when is set equal to unity, one recovers the field equations of f(T) gravity. We study in detail the cosmological evolution of the model in the presence of collisionless non-relativistic matter case, and we derive the exact forms of the dark energy density parameter and of the dark energy equation of state parameter, from which we impose constraints on the non-extensive thermodynamics parameter, δ, by using the Planck 2018 data on cosmological parameters. Accordingly, we repeat our calculations after including the relativistic matter along with the non-relativistic one, and we derive the new forms of the dark energy density parameter and of the dark energy equation of state parameter. Our study shows that the inclusion of non-extensive thermodynamic effects, quantified by the parameter δ, for a flat Friedmann-Robertson-Walker Universe, has measurable differences compared with the normal thermodynamics case. We confront our results with Type Ia supernovae observations for z≥0.4 and we obtain reasonably agreement with the observational data.

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Nonextensive statistical mechanics: Applications to high energy physics

Cited by 7 publications

References 60 publications

Scaling properties of rainfall induced landslides predicted by a physically based model

Scaling properties of rainfall induced landslides predicted by a physically based model

The Magnetic Field Effect on Thermodynamics of Hot QCD Matter using Extensive and non-Extensive Statistics

Non-Extensive Thermodynamics Effects in the Cosmology of f(T) Gravity

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