  It is often incorrectly assumed that the number of microstates \Omega
(E,V,N,...) available to an isolated system can have arbitrary dependence on
the extensive variables E,V,N, .... However, this is not the case for natural
systems which can reach thermodynamic equilibrium since restrictions exist
arising from the underlying equilibrium axioms of independence and \it{a
priori} equal probability of microstate, and the fundamental constants of
Nature. Here we derive a concise formula specifying the condition on \Omega
which must be met for real systems. Models which do not respect this condition
will present inconsistencies when treated under equilibrium thermodynamic
formalism. This has relevance to a number of recent models in which negative
heat capacity and violation of fundamental thermodynamic law have been
reported. Natural quantum systems obey the axioms and abide by the fundamental
constants, and thus natural systems, in the absence of infinite range forces,
can, in principle, attain thermodynamic equilibrium.
