Statistical mechanics of exploding phase spaces: Ontic open systems
  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. 
Henrik Jeldtoft Jensen, Roozbeh H. Pazuki, Gunnar Pruessner and   Piergiulio Tempesta
cond-mat.stat-mech