Abstract

The so-called Gibbs paradox is a paradigmatic narrative illustrating the necessity to account for
the N! ways of permuting N identical particles when summing over microstates. Yet, there exist
some mixing scenarios for which the expected thermodynamic outcome depends on the viewpoint
one chooses to justify this combinatorial term. After a brief summary on Gibbs' paradox and what is
the standard rationale used to justify its resolution, we will allow ourself to question from a historical
standpoint whether the Gibbs paradox has actually anything to do with Gibbs' work. In so doing,
we also aim at shedding a new light with regards to some of the theoretical claims surrounding its
resolution. We will then turn to the statistical thermodynamics of discrete and continuous mixtures
and introduce the notion of composition entropy to characterise these systems. This will enable us to
address, in a certain sense, a "curiosity" pointed out by Gibbs in a paper published in 1876. Finally,
we will �nish by proposing a connexion between the results we propose and a recent extension of
the Landauer bound regarding the minimum amount of heat to be dissipated to reset one bit of
memory.