Unique additive information measures—Boltzmann–Gibbs–Shannon, Fisher and beyond

Ván, P.

doi:10.1016/j.physa.2006.01.027

Cited by 7 publications

(3 citation statements)

References 28 publications

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“…A more prestigious attempt is to set such phenomena into a united framework of non-extensive thermodynamics, based on certain generalizations of familiar basic formulas. In particular generalizations of the Boltzmann -Gibbs -Shannon entropy formula were seeked as funding stones for such a general treatment [1,2,3,4,5,6,7,8].…”

Section: Introductionmentioning

confidence: 99%

Non-extensive approach to quark matter

2009

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We review the idea of generating non-extensive stationary distributions based on abstract composition rules of the subsystem energies, in particular the parton cascade method, using a Boltzmann equation with relativistic kinematics and modified two-body energy composition rules. The thermodynamical behavior of such model systems is investigated. As an application hadronic spectra with power-law tails are analyzed in the framework of a quark coalescence model. PACS. 21.65.Qr quark matter -25.75.Ag global features in relativistic heavy ion collisions -05.20.Dd kinetic theory

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Section: Introductionmentioning

confidence: 99%

Non-extensive approach to quark matter

2009

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“…Reversely, the additivity of entropy is -in some cases-achieved by non-product probabilities, trying to grasp the essence of surviving correlations (surmised to occur due to long-range interactions) in systems, which are large in the thermodynamical sense [24]. The additivity of entropy also can be achieved by weakly non-local extensions [25,26]. The connection between generalized, among them non-Boltzmannian probability distributions and the thermodynamic entropy formula was clarified in a recent paper [27].…”

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confidence: 99%

Abstract composition rule for relativistic kinetic energy in the thermodynamical limit

Bı́ró¹

2008

Europhys. Lett.

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We demonstrate by simple mathematical considerations that a power-law-tailed distribution in the kinetic energy of relativistic particles can be a limiting distribution seen in relativistic heavy-ion experiments. We prove that the infinite repetition of an arbitrary composition rule on an infinitesimal amount leads to a rule with a formal logarithm. As a consequence the stationary distribution of energy in the thermodynamical limit follows the composed function of the Boltzmann-Gibbs exponential with this formal logarithm. In particular, interactions described as solely functions of the relative four-momentum squared lead to kinetic energy distributions of the Tsallis-Pareto (cut power law) form in the high-energy limit.

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“…where the macro state of an N-particle physical system is given as D n . The distribution of N particles according to n class is shown as follows [9,10]:…”

Section: Definitionmentioning

confidence: 99%