  We present a thermodynamic formulation for scale-invariant systems based on
the minimization with constraints of Fisher's information measure. In such a
way a clear analogy between these systems's thermal properties and those of
gases and fluids is seen to emerge in natural fashion. We focus attention on
the non-interacting scenario, speaking thus of scale-free ideal gases (SFIGs)
and present some empirical evidences regarding such disparate systems as
electoral results, city populations and total citations in Physics journals,
that seem to indicate that SFIGs do exist. We also illustrate the way in which
Zipf's law can be understood in a thermodynamical context as the surface of a
finite system. Finally, we derive an equivalent microscopic description of our
systems which totally agrees with previous numerical simulations found in the
literature.
