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Motivated by the nonextensive nature of entropy in gravitational context andthe Gauge/Gravity duality, black hole thermodynamics has been attractingintense emphasis in the literature. Along the present work, we investigate somefeatures of the phase structure and critical phenomena of the 4-dimensionalcharged black holes in asymptotically flat spacetime within the formalism ofR\'enyi statistics. First, we explore the extended phase space via the R\'enyistatistics approach. Concretely, based on the modified version of the Smarrformula, we recall the equal-area law to remove the oscillatory non-physicalregion in the $P_R-V$ and $T_R-S_R$ planes. Then, the coexistence curves aredetermined, as well as the latent heat of phase change. Moreover, we prove thatthe critical exponent describing the behavior of the order parameter near thecritical point is $\frac{1}{2}$, which is consistent with Landau's theory ofcontinuous phase transition. Lastly, we apply the Hamiltonian approach toR\'enyi thermodynamics which provides a new and solid mathematical basis forthe extension of phase space and puts more insight into an expected andprofound possible connection between the nonextensivity R\'enyi parameter$\lambda$ and the cosmological constant $ \Lambda$.

On some phase equilibrium features of charged black holes in flat spacetime via R\'enyi statistics