2,392 research outputs found
Justification of Power-Law Canonical Distributions Based on Generalized Central Limit Theorem
A self-consistent thermodynamic framework is presented for power-law
canonical distributions based on the generalized central limit theorem by
extending the discussion given by Khinchin for deriving Gibbsian canonical
ensemble theory. The thermodynamic Legendre transform structure is invoked in
establishing its connection to nonextensive statistical mechanics.Comment: 8 pages. Some minor corrections are made, with no changes in the
conclusion
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
Tables of Hyperonic Matter Equation of State for Core-Collapse Supernovae
We present sets of equation of state (EOS) of nuclear matter including
hyperons using an SU_f(3) extended relativistic mean field (RMF) model with a
wide coverage of density, temperature, and charge fraction for numerical
simulations of core collapse supernovae. Coupling constants of Sigma and Xi
hyperons with the sigma meson are determined to fit the hyperon potential
depths in nuclear matter, U_Sigma(rho_0) ~ +30 MeV and U_Xi(rho_0) ~ -15 MeV,
which are suggested from recent analyses of hyperon production reactions. At
low densities, the EOS of uniform matter is connected with the EOS by Shen et
al., in which formation of finite nuclei is included in the Thomas-Fermi
approximation. In the present EOS, the maximum mass of neutron stars decreases
from 2.17 M_sun (Ne mu) to 1.63 M_sun (NYe mu) when hyperons are included. In a
spherical, adiabatic collapse of a 15 star by the hydrodynamics
without neutrino transfer, hyperon effects are found to be small, since the
temperature and density do not reach the region of hyperon mixture, where the
hyperon fraction is above 1 % (T > 40 MeV or rho_B > 0.4 fm^{-3}).Comment: 23 pages, 6 figures (Fig.3 and related comments on pion potential are
corrected in v3.
Liquid-Gas Phase Transition of Supernova Matter and Its Relation to Nucleosynthesis
We investigate the liquid-gas phase transition of dense matter in supernova
explosion by the relativistic mean field approach and fragment based
statistical model. The boiling temperature is found to be high (T_{boil} >= 0.7
MeV for rho_B >= 10^{-7} fm^{-3}), and adiabatic paths are shown to go across
the boundary of coexisting region even with high entropy. This suggests that
materials experienced phase transition can be ejected to outside. We calculated
fragment mass and isotope distribution around the boiling point. We found that
heavy elements at the iron, the first, second, and third peaks of r-process are
abundantly formed at rho_B = 10^{-7}, 10^{-5}, 10^{-3} and 10^{-2} fm^{-3},
respectively.Comment: 29 pages, 13 figures. This article is submitted to Nucl. Phys.
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