  We analytically investigate the thermodynamic variables of a hot and dense
system, in the framework of the Tsallis non-extensive classical statistics.
After a brief review, we start by recalling the corresponding massless limits
for all the thermodynamic variables. We then present the detail of calculation
for the exact massive result regarding the pressure -- valid for all values of
the $q$-parameter -- as well as the Tsallis $T$-, $\mu$- and $m$- parameters,
the former characterizing the non-extensivity of the system. The results for
other thermodynamic variables, in the massive case, readily follow from
appropriate differentiations of the pressure, for which we provide the
necessary formulas. For the convenience of the reader, we tabulate all of our
results. A special emphasis is put on the method used in order to perform these
computations, which happens to reduce cumbersome momentum integrals into
simpler ones. Numerical consistency between our analytic results and the
corresponding usual numerical integrals are found to be perfectly consistent.
Finally, it should be noted that our findings substantially simplify
calculations within the Tsallis framework. The latter being extensively used in
various different fields of science as for example, but not limited to,
high-energy nucleus collisions, we hope to enlighten a number of possible
applications.
