855 research outputs found
Generalized Kinetic Equations for a System of Interacting Atoms and Photons: Theory and Simulations
In the present paper we introduce generalized kinetic equations describing
the dynamics of a system of interacting gas and photons obeying to a very
general statistics. In the space homogeneous case we study the equilibrium
state of the system and investigate its stability by means of Lyapounov's
theory. Two physically relevant situations are discussed in details: photons in
a background gas and atoms in a background radiation. After having dropped the
statistics generalization for atoms but keeping the statistics generalization
for photons, in the zero order Chapmann-Enskog approximation, we present two
numerical simulations where the system, initially at equilibrium, is perturbed
by an external isotropic Dirac's delta and by a constant source of photons.Comment: 24 pages, 4 figures, IOP macro style, accepted on J. Phys. A: Math.
Ge
Canonical partition function for anomalous systems described by the -entropy
Starting from the -distribution function, obtained by applying the
maximal entropy principle to the -entropy [G. Kaniadakis, Phys. Rev. E
66 (2002), 056125], we derive the expression of the canonical
-partition function and discuss its main properties. It is shown that
all important macroscopical quantities of the system can be expressed employing
only the -partition function. The relationship between the associated
-free energy and the -entropy is also discussed.Comment: 8 pages, no figures. Work presented at the International conference
Complexity and Nonextensivity: New Trends in Statistical Mechanics. - Yukawa
Institute for Theoretical Physics - (14-18 March 2005) Kyoto, Japa
Lesche Stability of -Entropy
The Lesche stability condition for the Shannon entropy [B. Lesche, J. Stat.
Phys. 27, 419 (1982)], represents a fundamental test, for its experimental
robustness, for systems obeying the Maxwell-Boltzmann statistical mechanics. Of
course, this stability condition must be satisfied by any entropic functional
candidate to generate non-conventional statistical mechanics. In the present
effort we show that the -entropy, recently introduced in literature [G.
Kaniadakis, Phys. Rev. E 66, 056125 (2002)], satisfies the Lesche stability
condition.Comment: Presented at next2003, Second Sardinian International Conference on
News and Expectations in Thermostatistics, Villasimius (Cagliari) Italy,
21st-28th September 2003. In press Physica A (2004). Elsevier LaTeX macros,
10 pages, minor change
Deformed logarithms and entropies
By solving a differential-functional equation inposed by the MaxEnt principle
we obtain a class of two-parameter deformed logarithms and construct the
corresponding two-parameter generalized trace-form entropies. Generalized
distributions follow from these generalized entropies in the same fashion as
the Gaussian distribution follows from the Shannon entropy, which is a special
limiting case of the family. We determine the region of parameters where the
deformed logarithm conserves the most important properties of the logarithm,
and show that important existing generalizations of the entropy are included as
special cases in this two-parameter class.Comment: Presented at next2003, Second Sardinian International Conference on
News and Expectations in Thermostatistics, Villasimius (Cagliari) Italy,
21st-28th September 2003. In press Physica A (2004). Elsevier LaTeX macros,
11 pages, 1 figur
Classical q-deformed dynamics
On the basis of the quantum q-oscillator algebra in the framework of quantum
groups and non-commutative q-differential calculus, we investigate a possible
q-deformation of the classical Poisson bracket in order to extend a generalized
q-deformed dynamics in the classical regime. In this framework, classical
q-deformed kinetic equations, Kramers and Fokker-Planck equations, are also
studied.
Pacs: 05.20.Dd, 45.20.-d, 02.20.Uw
Keywords: Kinetic theory, q-deformed classical mechanics, quantum groups,
quantum algebrasComment: 8 pages, RevTex4; contribution to the international conference "Next
Sigma Phi" on News, EXpectations, and Trends in statistical physics, Crete
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