31 research outputs found
Foundation of Equilibrium Statistical Mechanics Based on Generalized Entropy
The general mathematical formulation of the equilibrium statistical mechanics based on the generalized statistical entropy for the first and second thermodynamic potentials was given. The Tsallis and Boltzmann-Gibbs statistical entropies in the canonical and microcanonical ensembles were investigated as an example. It was shown that the statistical mechanics based on the Tsallis statistical entropy satisfies the requirements of equilibrium thermodynamics in the thermodynamic limit if the entropic index z=1/(q-1) is an extensive variable of state of the system
Equilibrium statistical mechanics for incomplete nonextensive statistics
The incomplete nonextensive statistics in the canonical and microcanonical
ensembles is explored in the general case and in a particular case for the
ideal gas. By exact analytical results for the ideal gas it is shown that
taking the thermodynamic limit, with being an extensive variable of
state, the incomplete nonextensive statistics satisfies the requirements of
equilibrium thermodynamics. The thermodynamical potential of the statistical
ensemble is a homogeneous function of the first degree of the extensive
variables of state. In this case, the incomplete nonextensive statistics is
equivalent to the usual Tsallis statistics. If is an intensive variable of
state, i.e. the entropic index is a universal constant, the requirements of
the equilibrium thermodynamics are violated.Comment: 7 page
Extensive Renyi Statistics from Non-Extensive Entropy
We show that starting with either the non-extensive Tsallis entropy in Wang's
formalism or the extensive Renyi entropy, it is possible to construct the
equilibrium statistical mechanics with non-Gibbs canonical distribution
functions. The transformation formulas between Tsallis statistics and Renyi
statistics are presented. The one-particle distribution function in Renyi
statistics with extensive entropy for the classical ideal gas at finite
particle number develops a power-law tail for high momenta.Comment: 14 pages, 2 figures, LaTe
Transverse momentum distributions of hadrons in the Tsallis-1 and Tsallis-2 statistics
We considered the ultrarelativistic transverse momentum distributions of the Tsallis-1 and Tsallis-2 statistics using two regularization schemes. It was revealed that the cut-off parameter strongly influences the behavior of the transverse momentum distribution in both statistics. We have also found that the ultrarelativistic transverse momentum distribution of the Tsallis-1 statistics is transformed to the momentum distribution of the Tsallis-2 statistics by identifying q → 1/qc
Fractional exclusion statistics applied to relativistic nuclear matter
The effect of statistics of the quasiparticles in the nuclear matter at
extreme conditions of density and temperature is evaluated in the relativistic
mean-field model generalized to the framework of the fractional exclusion
statistics (FES). In the model, the nucleons are described as quasiparticles
obeying FES and the model parameters were chosen to reproduce the ground state
properties of the isospin-symmetric nuclear matter. In this case, the
statistics of the quasiparticles is related to the strengths of the
nucleon-nucleon interaction mediated by the neutral scalar and vector meson
fields. The relevant thermodynamic quantities were calculated as functions of
the nucleons density, temperature and fractional exclusion statistics parameter
. It has been shown that at high temperatures and densities the
thermodynamics of the system has a strong dependence on the statistics of the
particles. The scenario in which the nucleon-nucleon interaction strength is
independent of the statistics of particles was also calculated, but it leads in
general to unstable thermodynamics.Comment: 17 pages, 7 figure
Quantum Statistical Model of Nuclear Multifragmentation in the Canonical Ensemble Method
A quantum statistical model of nuclear multifragmentation is proposed. The
recurrence equation method used within the canonical ensemble makes the model
solvable and transparent to physical assumptions and allows to get results
without involving the Monte Carlo technique. The model exhibits the first order
phase transition. Quantum statistics effects are clearly seen on the
microscopic level of occupation numbers but are almost washed out for global
thermodynamic variables and the averaged observables studied. In the latter
case, the recurrence relations for multiplicity distributions of both
intermediate-mass and all fragments are derived and the specific changes in the
shape of multiplicity distributions in the narrow region of the transition
temperature is stressed. The temperature domain favorable to search for the HBT
effect is noted.Comment: 38 pages, 11 figure
Nonextensive statistical effects in the quark-gluon plasma formation at relativistic heavy-ion collisions energies
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 non-extensive statistical mechanics, characterized by power-law quantum
distributions. We impose the Gibbs conditions on the global conservation of
baryon number, electric charge and strangeness number. For the hadronic phase,
we study an extended relativistic mean-field theoretical model with the
inclusion of strange particles (hyperons and mesons). For the quark sector, we
employ an extended MIT-Bag model. In this context we focus on the relevance of
non-extensive effects in the presence of strange matter.Comment: 12 pages, 5 figure
Modified Hagedorn formula including temperature fluctuation - Estimation of temperatures at RHIC experiments -
We have systematically estimated the possible temperatures obtained from an
analysis of recent data on distributions observed at RHIC experiments.
Using the fact that observed distributions cannot be described by the
original Hagedorn formula in the whole range of transverse momenta (in
particular above 6 GeV/c), we propose a modified Hagedorn formula including
temperature fluctuation. We show that by using it we can fit
distributions in the whole range and can estimate consistently the relevant
temperatures, including their fluctuations.Comment: Some misprints corrected, references updated. To be published in Eur.
Phys. J. C (2006
Number Fluctuation and the Fundamental Theorem of Arithmetic
We consider N bosons occupying a discrete set of single-particle quantum
states in an isolated trap. Usually, for a given excitation energy, there are
many combinations of exciting different number of particles from the ground
state, resulting in a fluctuation of the ground state population. As a counter
example, we take the quantum spectrum to be logarithms of the prime number
sequence, and using the fundamental theorem of arithmetic, find that the ground
state fluctuation vanishes exactly for all excitations. The use of the standard
canonical or grand canonical ensembles, on the other hand, gives substantial
number fluctuation for the ground state. This difference between the
microcanonical and canonical results cannot be accounted for within the
framework of equilibrium statistical mechanics.Comment: 4 pages, 4 figures. To be submitted to Phys. Rev. Let
Thermodynamic Derivation of the Tsallis and R\'enyi Entropy Formulas and the Temperature of Quark-Gluon Plasma
We derive Tsallis entropy, Sq, from universal thermostat independence and
obtain the functional form of the corresponding generalized entropy-probability
relation. Our result for finite thermostats interprets thermodynamically the
subsystem temperature, T1, and the index q in terms of the temperature, T,
entropy, S, and heat capacity, C of the reservoir as T1 = T exp(-S/C) and q = 1
- 1/C. In the infinite C limit, irrespective to the value of S, the
Boltzmann-Gibbs approach is fully recovered. We apply this framework for the
experimental determination of the original temperature of a finite thermostat,
T, from the analysis of hadron spectra produced in high energy collisions, by
analyzing frequently considered simple models of the quark-gluon plasma.Comment: 4 pages 1 Figure PRL style, revised presentatio