  We studied the Sharma-Mittal relative entropy and showed that its physical
meaning is the free energy difference between the off-equilibrium and
equilibrium distributions. Unfortunately, Sharma-Mittal relative entropy may
acquire this physical interpretation only in the limiting case when both
parameters approach to 1 in which case it approaches Kullback-Leibler entropy.
We also note that this is exactly how R\'{e}nyi relative entropy behaves in the
thermostatistical framework thereby suggesting that Sharma-Mittal entropy must
be thought to be a step beyond not both Tsallis and R\'{e}nyi entropies but
rather only as a generalization of R\'{e}nyi entropy from a thermostatistical
point of view. Lastly, we note that neither of them conforms to the
Shore-Johnson theorem which is satisfied by Kullback-Leibler entropy and one of
the Tsallis relative entropies.
