Volume of classical and quantum ensembles: geometric approach to entropy   and information
  It is shown for classical and quantum ensembles that there is a unique quantity which has the properties of a "volume". This quantity is a function of the ensemble entropy, and hence provides a geometric interpretation for the latter. It further provides a geometric picture for deriving and unifying a number of results in classical and quantum information theory, and for discussing entropic uncertainty relations. 
Michael J.W. Hall