  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.
