Tsallis entropy and the Vlasov-Poisson equations

Plastino, A.; Plastino, A.

doi:10.1590/s0103-97331999000100008

Cited by 32 publications

(32 citation statements)

References 1 publication

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“…As a special instance of Eqs. (16), (17) and (19), let us discuss the canonical ensemble. In this case, only a single constraint regarding the system Hamiltonian is considered.…”

Section: Brief Review Olm Formalismmentioning

confidence: 99%

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Classical gas in nonextensive optimal Lagrange multipliers formalism

et al. 2001

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“…As a special instance of Eqs. (16), (17) and (19), let us discuss the canonical ensemble. In this case, only a single constraint regarding the system Hamiltonian is considered.…”

Section: Brief Review Olm Formalismmentioning

confidence: 99%

“…Tsallis' thermostatistics [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] is by now known to offer a nonextensive generalization of traditional BoltzmannGibbs statistical mechanics. A key ingredient in this formalism is the introduction of a particular definition of expectation value termed the normalized q-expectation value [4].…”

Section: Introductionmentioning

confidence: 99%

Classical gas in nonextensive optimal Lagrange multipliers formalism

et al. 2001

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“…Indeed, it is too often ignored that classical thermodynamics does not hold for gravitating systems, because these are nonextensive in the thermodynamical sense (Landsberg 1972(Landsberg , 1984Tsallis 1999;Plastino & Plastino 1999). Actually, many other natural systems do not respect the requisites of thermodynamics.…”

Section: Introductionmentioning

confidence: 99%

Long-range correlations in self-gravitatingN-body systems

Huber

Pfenniger

2002

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Abstract. Observed self-gravitating systems reveal often fragmented, non-equilibrium structures that feature characteristic long-range correlations. However, models accounting for non-linear structure growth are not always consistent with observations and a better understanding of self-gravitating N-body systems appears necessary. Because unstable gravitating systems are sensitive to non-gravitational perturbations, we study the effect of different dissipative factors as well as different small and large scale boundary conditions on idealized N-body systems. We find, in the interval of negative specific heat, equilibrium properties differing from theoretical predictions made for gravo-thermal systems, substantiating the importance of microscopic physics and the lack of consistent theoretical tools to describe self-gravitating gas. Also, in the interval of negative specific heat, yet outside of equilibrium, unforced systems fragment and establish transient long-range correlations. The strength of these correlations depends on the degree of granularity, which shows that the mass and force resolution should be coherent. Finally, persistent correlations appear in model systems subject to an energy flow.

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“…The Tsallis nonextensive approach to the Vlasov-Poisson equations will be considered for the general case of D spatial dimensions, in order to provide an illustrative example of a problem where Tsallis parameter q depends on the spatial dimentionality. Similar calculations using Tsallis formalism with unnormalized q-constraints can be found in [77].…”

Section: Tsallis Nonextensive Thermostatistics and The Vlasov-poissonmentioning

confidence: 55%

III. Tsallis Theory, the Maximum Entropy Principle, and Evolution Equations

Plastino¹

2001

Nonextensive Statistical Mechanics and Its Applications

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Abstract. The generalized thermostatistics advanced by Tsallis in order to treat nonextensive systems has greatly increased the range of possible applications of statistical mechanics to the description of natural phenomena. Here we consider some aspects of the relationship between Tsallis' theory and Jaynes' maximum entropy (MaxEnt) principle. We review some universal properties of general thermostatistical formalisms based on an entropy extremalization principle. We explain how Tsallis formalism provides a useful tool in order to obtain MaxEnt solutions of nonlinear partial differential equations describing nonextensive physical systems. In particular, we consider the case of the Vlasov-Poisson equations, where Tsallis MaxEnt principle leads in a natural way to the stellar polytrope solutions. We pay special attention to the "P -picture" formulation of Tsallis generalized thermostatistics based on the entropic functionalS q and standard linear constraints.

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Tsallis entropy and the Vlasov-Poisson equations

Cited by 32 publications

References 1 publication

Classical gas in nonextensive optimal Lagrange multipliers formalism

Classical gas in nonextensive optimal Lagrange multipliers formalism

Long-range correlations in self-gravitatingN-body systems

III. Tsallis Theory, the Maximum Entropy Principle, and Evolution Equations

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