  The volume of phase space may grow super-exponentially ("explosively") with
the number of degrees of freedom for certain types of complex systems such as
those encountered in biology and neuroscience, where components interact and
create new emergent states. Standard ensemble theory can break down as we
demonstrate in a simple model reminiscent of complex systems where new
collective states emerge. We present an axiomatically defined entropy and argue
that it is extensive in the micro-canonical, equal probability, and canonical
(max-entropy) ensemble for super-exponentially growing phase spaces. This
entropy may be useful in determining probability measures in analogy with how
statistical mechanics establishes statistical ensembles by maximising entropy.
