  The underlying connection between the degrees of freedom of a system and its
nonextensive thermodynamic behavior is addressed. The problem is handled by
starting from a thermodynamical system with fractal structure and its
analytical reduction to a finite ideal gas. In the limit where the
thermofractal has no internal structure, it is found that it reproduces the
basic properties of a nonextensive ideal gas with a finite number of particles
as recently discussed (Lima \& Deppman, Phys. Rev. E 101, 040102(R) 2020). In
particular, the entropic $q$-index is calculated in terms of the number of
particles both for the nonrelativistic and relativistic cases. In light of such
results, the possible nonadditivity or additivity of the entropic structures
are also critically analysed and new expressions to the entropy (per particle)
for a composed system of thermofractals and its limiting case are derived.
