  The appearance of dark sunspots over the solar photosphere is not considered
to be symmetric between the northern and southern hemispheres. Among the
different conclusions obtained by several authors, we can point out that the
North-South asymmetry is a real and systematic phenomenon and is not due to
random variability. In the present work, we selected the sunspot area data of a
sample of 13 solar cycles divided by hemisphere extracted from the Marshall
Space Flight Centre (MSFC) database to investigate the behavior of probability
distributions using an out-of-equilibrium statistical model a.k.a non-extensive
statistical mechanics. Based on this statistical framework, we obtained that
the non-extensive entropic parameter $q$ has a semi-sinusoidal variation with a
period of $\sim$22 year (Hale cycle). Among the most important results, we can
highlight that the asymmetry index $q(A)$ revealed the dominance of the
northern hemisphere against the southern one. Thus, we concluded that the
parameter $q(A)$ can be considered an effective measure for diagnosing
long-term variations of the solar dynamo. Finally, our study opens a new
approach to investigating solar variability from the nonextensive perspective.
