Solid/Liquid Phase Transition and Heat Engine in Asymptotically Flat Schwarzschild Black Hole via the Rényi Extended Phase Space Approach (2106.02406v2)

Abstract: Recently, it has been found that, with the R\'enyi statistics, the asymptotically flat Schwarzschild black hole can be in thermal equilibrium with infinite heat reservior at a fixed temperature when its event horizon radius is larger than the characteristic length scale $L_\lambda=1/\sqrt{\pi \lambda}$, where $\lambda$ is the nonextensivity parameter. In the R\'enyi extended phase space with the $PdV$ work term, an off-shell free energy in the canonical ensemble with the thermodynamic volume as an order parameter is considered to identify a first-order Hawking-Page (HP) phase transition as a solid/liquid phase transition. It has the latent heat of fusion from solid (corresponding to thermal radiation) to liquid (corresponding to black hole) in the form of $\sim 1/\sqrt{\lambda}$; this is evident of the absence of the HP phase transition in the case of asymptotically flat Schwarzschild black hole from the GB statistics ($\lambda=0$). Moreover, we investigate the generalized second law of black hole thermodynamics (GSL) in R\'enyi statistics by considering the black hole as a working substance in heat engine. Interestingly, an efficiency $\eta$ of the black hole in a Carnot cycle takes the form $\eta_c=1-T_\text{C}/T_\text{H}$. This confirms the validity of the GSL in the R\'enyi extended phase space.