  Prompted by the realisation that the statistical entropy of an ideal gas in
the micro-canonical ensemble should not fluctuate or change over time, the
meaning of the H-theorem is re-interpreted from the perspective of information
theory in which entropy is a measure of uncertainty. We propose that the
Maxwellian velocity distribution should more properly be regarded as a limiting
distribution which is identical with the distribution across particles in the
asymptotic limit of large numbers. In smaller systems, the distribution across
particles differs from the limiting distribution and fluctuates. Therefore the
entropy can be calculated either from the actual distribution across the
particles or from the limiting distribution. The former fluctuates with the
distribution but the latter does not. However, only the latter represents
uncertainty in the sense implied by information theory by accounting for all
possible microstates. We also argue that the Maxwellian probability
distribution for the velocity of a single particle should be regarded as a
limiting distribution. Therefore the entropy of a single particle is well
defined, as is the entropy of an N-particle system, regardless of the
microstate. We argue that the meaning of the H-theorem is to reveal the
underlying distribution in the limit of large numbers. Computer simulations of
a hard-sphere fluid are used to demonstrate the ideas.
