199 research outputs found
Nonextensive quasiparticle description of QCD matter
The dynamics of QCD matter is often described using effective mean field (MF)
models based on Boltzmann-Gibbs (BG) extensive statistics. However, such matter
is normally produced in small packets and in violent collisions where the usual
conditions justifying the use of BG statistics are not fulfilled and the
systems produced are not extensive. This can be accounted for either by
enriching the original dynamics or by replacing the BG statistics by its
nonextensive counterpart described by a nonextensivity parameter (for
one returns to the extensive situation). In this work we investigate
the interplay between the effects of dynamics and nonextensivity. Since the
complexity of the nonextensive MF models prevents their simple visualization,
we instead use some simple quasi-particle description of QCD matter in which
the interaction is modelled phenomenologically by some effective fugacities,
. Embedding such a model in a nonextensive environment allows for a
well-defined separation of the dynamics (represented by ) and the
nonextensivity (represented by ) and a better understanding of their
relationship.Comment: Thorougly reworked version published in Symmetry 2019, 11(3), 401, as
contribution to the Special Issue Nambu--Jona-Lassinio model and its
applications; 22 pages, 7 figure
Nonextensive statistical effects in the hadron to quark-gluon phase transition
We investigate the relativistic equation of state of hadronic matter and
quark-gluon plasma at finite temperature and baryon density in the framework of
the nonextensive statistical mechanics, characterized by power-law quantum
distributions. We study the phase transition from hadronic matter to
quark-gluon plasma by requiring the Gibbs conditions on the global conservation
of baryon number and electric charge fraction. We show that nonextensive
statistical effects play a crucial role in the equation of state and in the
formation of mixed phase also for small deviations from the standard
Boltzmann-Gibbs statistics.Comment: 13 pages, 10 figure
Nonextensive Nambu Jona-Lasinio model of QCD matter revisited
We present a revisited version of the nonextensive QCD-based Nambu -
Jona-Lasinio (NJL) model describing the behavior of strongly interacting matter
proposed by us some time ago. As before, it is based on the nonextensive
generalization of the Boltzmann-Gibbs (BG) statistical mechanics used in the
NJL model to its nonextensive version based on Tsallis statistics, but this
time it fulfils the basic requirements of thermodynamical consistency.
Different ways in which this can be done, connected with different possible
choices of the form of the corresponding nonextensive entropies, are presented
and discussed in detail. The corresponding results are compared, discussed and
confronted with previous findings.Comment: 16 pages, 18 figures minor revision, to be published in EPJ
Many-body q-exponential distribution prescribed by factorization hypothesis
The factorization problem of -exponential distribution within nonextensive
statistical mechanics is discussed on the basis of Abe's general
pseudoadditivity for equilibrium systems. it is argued that the factorization
of compound probability into product of the probabilities of subsystems is
nothing but the consequence of existence of thermodynamic equilibrium in the
interacting systems having Tsallis entropy. So the factorization does not needs
independent noninteracting systems and should be respected in all exact
calculations concerning interacting nonextensive subsystems. This consideration
makes it legitimate to use -exponential distribution either for composite
system or for single body in many-body systems. Some known results of ideal
gases obtained with additive energy are reviewed.Comment: 13 pages, no figure, RevTe
Quasicanonical Gibbs distribution and Tsallis nonextensive statistics
We derive and study quasicanonical Gibbs distribution function which is
characterized by the thermostat with finite number of particles
(quasithermostat). We show that this naturally leads to Tsallis nonextensive
statistics and thermodynamics, with Tsallis parameter q is found to be related
to the number of particles in the quasithermostat. We show that the chi-square
distribution of fluctuating temperature used recently by Beck can be partially
understood in terms of normal random momenta of particles in the
quasithermostat. Also, we discuss on the importance of the time scale hierarchy
and fluctuating probability distribution functions in understanding of Tsallis
distribution, within the framework of kinetics of dilute gas and weakly
inhomogeneous systems.Comment: 22 pages, 1 eps-figur
Nonextensive statistics: Theoretical, experimental and computational evidences and connections
The domain of validity of standard thermodynamics and Boltzmann-Gibbs
statistical mechanics is discussed and then formally enlarged in order to
hopefully cover a variety of anomalous systems. The generalization concerns
{\it nonextensive} systems, where nonextensivity is understood in the
thermodynamical sense. This generalization was first proposed in 1988 inspired
by the probabilistic description of multifractal geometries, and has been
intensively studied during this decade. In the present effort, after
introducing some historical background, we briefly describe the formalism, and
then exhibit the present status in what concerns theoretical, experimental and
computational evidences and connections, as well as some perspectives for the
future. In addition to these, here and there we point out various (possibly)
relevant questions, whose answer would certainly clarify our current
understanding of the foundations of statistical mechanics and its
thermodynamical implicationsComment: 15 figure
Tsallis Ensemble as an Exact Orthode
We show that Tsallis ensemble of power-law distributions provides a
mechanical model of nonextensive equilibrium thermodynamics for small
interacting Hamiltonian systems, i.e., using Boltzmann's original nomenclature,
we prove that it is an exact orthode. This means that the heat differential
admits the inverse average kinetic energy as an integrating factor. One
immediate consequence is that the logarithm of the normalization function can
be identified with the entropy, instead of the q-deformed logarithm. It has
been noted that such entropy coincides with Renyi entropy rather than Tsallis
entropy, it is non-additive, tends to the standard canonical entropy as the
power index tends to infinity and is consistent with the free energy formula
proposed in [S. Abe et. al. Phys. Lett. A 281, 126 (2001)]. It is also shown
that the heat differential admits the Lagrange multiplier used in non-extensive
thermodynamics as an integrating factor too, and that the associated entropy is
given by ordinary nonextensive entropy. The mechanical approach proposed in
this work is fully consistent with an information-theoretic approach based on
the maximization of Renyi entropy.Comment: 5 pages. Added connection with Renyi entrop
Nonlinear statistical effects in relativistic mean field theory
We investigate the relativistic mean field theory of nuclear matter at finite
temperature and baryon density taking into account of nonlinear statistical
effects, characterized by power-law quantum distributions. The analysis is
performed by requiring the Gibbs conditions on the global conservation of
baryon number and electric charge fraction. We show that such nonlinear
statistical effects play a crucial role in the equation of state and in the
formation of mixed phase also for small deviations from the standard
Boltzmann-Gibbs statistics.Comment: 9 pages, 5 figures. arXiv admin note: substantial text overlap with
arXiv:1005.4643 and arXiv:0912.460
- …