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From the viewpoint of holography, the phase structure of a 5-dimensional Reissner-Nordström-AdS black hole is probed by the two-point correlation function, Wilson loop, and entanglement entropy. As the case of thermal entropy, we find for all the probes that the black hole undergoes a Hawking-Page phase transition, a first-order phase transition, and a second-order phase transition successively before it reaches a stable phase. In addition, for these probes, we find that the equal area law for the first-order phase transition is valid always and the critical exponent of the heat capacity for the second-order phase transition coincides with that of the mean field theory regardless of the size of the boundary region.

Loop quantum cosmology (LQC) is very powerful to deal with the behavior of early universe. And the effective loop quantum cosmology gives a successful description of the universe in the semiclassical region. We consider the apparent horizon of the Friedmann-Robertson-Walker universe as a thermodynamical system and investigate the thermodynamics of LQC in the semiclassical region. The effective density and effective pressure in the modified Friedmann equation from LQC not only determine the evolution of the universe in LQC scenario but are actually also found to be the thermodynamic quantities. This result comes from the energy definition in cosmology (the Misner-Sharp gravitational energy) and is consistent with thermodynamic laws. We prove that within the framework of loop quantum cosmology, the elementary equation of equilibrium thermodynamics is still valid., Comment: 4 pages