1,871 research outputs found
Intensive variables in the framework of the non-extensive thermostatistics
By assuming an appropriate energy composition law between two systems
governed by the same non-extensive entropy, we revisit the definitions of
temperature and pressure, arising from the zeroth principle of thermodynamics,
in a manner consistent with the thermostatistics structure of the theory. We
show that the definitions of these quantities are sensitive to the composition
law of entropy and internal energy governing the system. In this way, we can
clarify some questions raised about the possible introduction of intensive
variables in the context of non-extensive statistical mechanics.Comment: 14 pages, elsart style, version accepted on Physics Letters
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
A mechanism to derive multi-power law functions: an application in the econophysics framework
It is generally recognized that economical systems, and more in general
complex systems, are characterized by power law distributions. Sometime, these
distributions show a changing of the slope in the tail so that, more
appropriately, they show a multi-power law behavior. We present a method to
derive analytically a two-power law distribution starting from a single power
law function recently obtained, in the frameworks of the generalized
statistical mechanics based on the Sharma-Taneja-Mittal information measure. In
order to test the method, we fit the cumulative distribution of personal income
and gross domestic production of several countries, obtaining a good agreement
for a wide range of data.Comment: 10pages, 3 figures. Presented at Int. Conf. on Application of Physics
in Financial Analisys (APFA5), June 29 - July 1, 2006 Torino, Ital
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
Quantum Orthogonal Planes: ISO_{q,r}(N) and SO_{q,r}(N) -- Bicovariant Calculi and Differential Geometry on Quantum Minkowski Space
We construct differential calculi on multiparametric quantum orthogonal
planes in any dimension N. These calculi are bicovariant under the action of
the full inhomogeneous (multiparametric) quantum group ISO_{q,r}(N), and do
contain dilatations.
If we require bicovariance only under the quantum orthogonal group
SO_{q,r}(N), the calculus on the q-plane can be expressed in terms of its
coordinates x^a, differentials dx^a and partial derivatives \partial_a without
the need of dilatations, thus generalizing known results to the multiparametric
case. Using real forms that lead to the signature (n+1,m) with m = n-1, n, n+1
, we find ISO_{q,r}(n+1, m) and SO_{q,r}(n+1,m) bicovariant calculi on the
multiparametric quantum spaces. The particular case of the quantum Minkowski
space ISO_{q,r}(3,1)/SO_{q,r}(3,1) is treated in detail.
The conjugated partial derivatives \partial_a* can be expressed as linear
combinations of the \partial_a. This allows a deformation of the phase-space
where no additional operators (besides x^a and p_a) are needed.Comment: LaTeX, 36 pages. Considered more real forms, added some explicit
formulas, used simpler definition of hermitean momenta. To be published in
European Phys. Jou.
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
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