  The exact forms of the degenerate Maxwell-Boltzmann (MB), Bose-Einstein (BE)
and Fermi-Dirac (FD) entropy functions, derived by Boltzmann's principle
without the Stirling approximation (Niven, Physics Letters A, 342(4) (2005)
286), are further examined. Firstly, an apparent paradox in quantisation
effects is resolved using the Laplace-Jaynes interpretation of probability. The
energy cost of learning that a system, distributed over s equiprobable states,
is in one such state (an s-fold decision) is then calculated for each
statistic. The analysis confirms that the cost depends on one's knowledge of
the number of entities N and (for BE and FD statistics) the degeneracy,
extending the findings of Niven (2005).
