  Identical classical particles are distinguishable. This distinguishability
affects the number of ways W a macrostate can be realized on the micro-level,
and from the relation S = k ln W leads to a non-extensive expression for the
entropy. This result is usually considered incorrect because of its
inconsistency with thermodynamics. It is sometimes concluded from this
inconsistency that identical particles are fundamentally indistinguishable
after all; and even that quantum mechanics is indispensable for making sense of
this. In contrast, we argue that the classical statistics of distinguishable
particles and the resulting non-extensive entropy function are perfectly
acceptable from both a theoretical and an experimental perspective. The
inconsistency with thermodynamics can be removed by taking into account that
the entropy concept in statistical mechanics is not completely identical to the
thermodynamical one. We observe that even identical quantum particles are in
some cases distinguishable, and conclude that quantum mechanics is irrelevant
to the Gibbs paradox.
