  The phase structure and critical phenomena of the 3+1 dimensional charged
black holes in asymptotically flat spacetime are investigated in terms of
thermodynamic properties within the R\'enyi statistics. With this approach as
the non-extensive parameter above zero, we find that the charged black hole can
be in thermodynamic equilibrium with surrounding thermal radiation, and have a
Hawking-Page phase transition in the same way in the case of AdS charged black
hole. This gives more evidence supporting the proposal that there exists an
equivalence between the black hole thermodynamics in asymptotically flat
spacetime via R\'enyi statistics and that in asymptotically AdS spacetime via
Gibbs-Boltzmann statistics, proposed by Czinner et al. However, the present
work also provides another aspect of supporting evidence through exploring the
extended phase space within the R\'enyi statistics. Working on a modified
version of Smarr formula, the thermodynamic pressure $P$ and volume $v$ of a
charged black hole are found to be related to the non-extensive parameter. The
resulting $P-v$ diagram indicates that the thermodynamics of charged black
holes in asymptotically flat spacetime via R\'enyi statistics has the Van der
Waals phase structure, equivalent to that in asymptotically AdS spacetime via
Gibbs-Boltzmann statistics.
