Recently, it has been found that, with the Renyi 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 Renyi 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 Renyi 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 Renyi extended phase space.
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