  In ordinary Boltzmann-Gibbs thermostatistics, the relative entropy expression
plays the role of generalized free energy, providing the difference between the
off-equilibrium and equilibrium free energy terms associated with
Boltzmann-Gibbs entropy. In this context, we studied whether this physical
meaning can be given to R\'{e}nyi relative entropy definition found in the
literature from a generalized thermostatistical point of view. We find that
this is possible only in the limit as $q$ approaches to 1. This shows that
R\'{e}nyi relative entropy has a physical (thermostatistical) meaning only when
the system can already be explained by ordinary Boltzmann-Gibbs
thermostatistics. Moreover, this can be taken as an indication of R\'{e}nyi
entropy being an equilibrium entropy since any relative entropy definition is a
two-probability generalization of the associated entropy definition. We also
note that this result is independent of the internal energy constraint
employed. Finally, we comment on the lack of foundation of R\'{e}nyi relative
entropy as far as its minimization (which is equivalent to the maximization of
R\'{e}nyi entropy) is considered in order to obtain a stationary equilibrium
distribution since R\'{e}nyi relative entropy does not conform to Shore-Johnson
axioms.
