The phase structure and critical phenomena of the 3 þ 1 dimensional charged black holes in asymptotically flat spacetime are investigated within the Rényi statistics. As the nonextensive parameter λ above zero, a charged black hole can be in thermodynamic equilibrium with surrounding thermal radiation and have a Hawking-Page phase transition. This gives more evidence supporting the proposed conjectured equivalence between the black hole thermodynamics in asymptotically flat spacetime via Rényi statistics and that in asymptotically anti-de Sitter (AdS) spacetime via Gibbs-Boltzmann statistics. The present work also provides another aspect of supporting evidence through exploring the extended phase space within the Rényi statistics. Working on a modified version of the Smarr formula, the thermodynamic pressure P and volume v of a charged black hole are found to be related to λ. The thermodynamics of asymptotically flat charged black holes via Rényi statistics has the Van der Waals phase structure, P − v criticality and universal constant, in a similar way as that of asymptotically AdS charged black hole via Gibbs-Boltzmann statistics. This raises an interesting question of how λ in the former system relates to jΛj in the latter one.

In the deconfined phase of quark-gluon plasma, it seems that most of the quarks, antiquarks and gluons should be effectively free in the absence of the linear confining potential. However, the remaining Coulomb-type potential between quarks in the plasma could still be sufficiently strong that certain bound states, notably of heavy quarks such as J/ψ are stable even in the deconfined plasma up to a certain temperature. Baryons can also exist in the deconfined phase provided that the density is sufficiently large. We study three kinds of exotic multi-quark bound states in the deconfined phase of quarkgluon plasma from gravity dual models in addition to the normal baryon. They are k-baryon, (N +k)-baryon and a bound state of j mesons which we call "j-mesonance". Binding energies and screening lengths of these exotic states are studied and are found to have similar properties to those of mesons and baryons at the leading order. Phase diagram for the exotic nuclear phases is subsequently studied in the Sakai-Sugimoto model. Even though the exotics are less stable than normal baryons, in the region of high chemical potential and low temperature, they are more stable thermodynamically than the vacuum and chiral-symmetric quark-gluon plasma phases (χS-QGP). *

We study thermodynamic properties of the multiquark nuclear matter. The dependence of the equation of state on the colour charges is explored both analytically and numerically in the limits where the baryon density is small and large at fixed temperature between the gluon deconfinement and chiral symmetry restoration. The gravitational stability of the hypothetical multiquark stars are discussed using the Tolman-Oppenheimer-Volkoff equation. Since the equations of state of the multiquarks can be well approximated by different power laws for small and large density, the content of the multiquark stars has the core and crust structure. We found that most of the mass of the star comes from the crust region where the density is relatively small. The mass limit of the multiquark star is determined as well as its relation to the star radius. For typical energy density scale of 10 GeV/fm 3 , the converging mass and radius of the hypothetical multiquark star in the limit of large central density are approximately 2.6−3.9 solar mass and 15-27 km. The adiabatic index and sound speed distributions of the multiquark matter in the star are also calculated and discussed. The sound speed never exceeds the speed of light and the multiquark matters are thus compressible even at high density and pressure. *

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