The nonextensive Thomas-Fermi theory in an n-dimensional space

We present a generalization of the extended nonextensive Thomas-Fermi model with thermal effects to n-dimensional space. A generalized Thomas-Fermi equation is derived. It is shown that both the linearities (thermal and nonextensive) are independent on the dimensionality of the space. It is also shown that for n=2, we have only nonextensive corrections, without the usual thermal correction term. The nonextensive corrections appear therefore to be a good correction and a way to include thermal effects in the two-dimensional Thomas-Fermi treatment for compact systems, such as graphene.