846 research outputs found
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
Stabilities of generalized entropies
The generalized entropic measure, which is optimized by a given arbitrary
distribution under the constraints on normalization of the distribution and the
finite ordinary expectation value of a physical random quantity, is considered
and its Lesche stability property (that is different from thermodynamic
stability) is examined. A general condition, under which the generalized
entropy becomes stable, is derived. Examples known in the literature, including
the entropy for the stretched-exponential distribution, the quantum-group
entropy, and the kappa-entropy are discussed.Comment: 16 pages, no figure
Composition law of -entropy for statistically independent systems
The intriguing and still open question concerning the composition law of
-entropy with and is here
reconsidered and solved. It is shown that, for a statistical system described
by the probability distribution , made up of two statistically
independent subsystems, described through the probability distributions and , respectively, with , the joint entropy
can be obtained starting from the and
entropies, and additionally from the entropic functionals
and , being
the -Napier number. The composition law of the -entropy is
given in closed form, and emerges as a one-parameter generalization of the
ordinary additivity law of Boltzmann-Shannon entropy recovered in the limit.Comment: 14 page
A new one parameter deformation of the exponential function
Recently, in the ref. Physica A \bfm{296} 405 (2001), a new one parameter
deformation for the exponential function , which presents a power law
asymptotic behaviour, has been proposed. The statistical distribution
, has been obtained
both as stable stationary state of a proper non linear kinetics and as the
state which maximizes a new entropic form. In the present contribution,
starting from the -algebra and after introducing the -analysis,
we obtain the -exponential as
the eigenstate of the -derivative and study its main mathematical
properties.Comment: 5 pages including 2 figures. Paper presented in NEXT2001 Meetin
Nonlinear gauge transformation for a class of Schroedinger equations containing complex nonlinearities
We consider a wide class of nonlinear canonical quantum systems described by
a one-particle Schroedinger equation containing a complex nonlinearity. We
introduce a nonlinear unitary transformation which permits us to linearize the
continuity equation. In this way we are able to obtain a new quantum system
obeying to a nonlinear Schroedinger equation with a real nonlinearity. As an
application of this theory we consider a few already studied Schroedinger
equations as that containing the nonlinearity introduced by the
exclusion-inclusion principle, the Doebner-Goldin equation and others.
PACS numbers: 03.65.-w, 11.15.-qComment: 3pages, two columns, RevTeX4, no figure
Kinetical Foundations of Non Conventional Statistics
After considering the kinetical interaction principle (KIP) introduced in
ref. Physica A {\bf296}, 405 (2001), we study in the Boltzmann picture, the
evolution equation and the H-theorem for non extensive systems. The
-kinetics and the -kinetics are studied in detail starting from the
most general non linear Boltzmann equation compatible with the KIP.Comment: 11 pages, no figures. Contribution paper to the proseedings of the
International School and Workshop on Nonextensive Thermodynamics and Physical
Applications, NEXT 2001, 23-30 May 2001, Cagliari Sardinia, Italy (Physica A
Nonlinear Transformation for a Class of Gauged Schroedinger Equations with Complex Nonlinearities
In the present contribution we consider a class of Schroedinger equations
containing complex nonlinearities, describing systems with conserved norm
and minimally coupled to an abelian gauge field. We introduce a
nonlinear transformation which permits the linearization of the source term in
the evolution equations for the gauge field, and transforms the nonlinear
Schroedinger equations in another one with real nonlinearities. We show that
this transformation can be performed either on the gauge field or,
equivalently, on the matter field . Since the transformation does not
change the quantities and , it can be considered a
generalization of the gauge transformation of third kind introduced some years
ago by other authors.
Pacs numbers: 03.65.-w, 11.15.-qComment: 4pages, two columns, RevTeX4, no figure
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