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

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

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.

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$M_\odot$ 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.

Nucleosynthesis in Outflows from the Inner Regions of Collapsars

We consider nucleosynthesis in outflows originating from the inner regions of viscous accretion disks formed after the collapse of a rotating massive star. We show that wind-like outflows driven by viscous and neutrino heating can efficiently synthesize Fe-group elements moving at near-relativistic velocities. The mass of 56Ni synthesized and the asymptotic velocities attained in our calculations are in accord with those inferred from observations of SN1998bw and SN2003dh. These steady wind-like outflows are generally proton rich, characterized by only modest entropies, and consequently synthesize essentially nothing heavier than the Fe-group elements. We also discuss bubble-like outflows resulting from rapid energy deposition in localized regions near or in the accretion disk. These intermittent ejecta emerge with low electron fraction and are a promising site for the synthesis of the A=130 r-process peak elements.Comment: 35 pages, 6 figures, added discussion of the influence of nuclear recombination on wind dynamics, to appear in Ap