Gibbs' Paradox according to Gibbs and slightly beyond

<p>The so-called Gibbs paradox is a paradigmatic narrative illustrating the necessity to account forthe N! ways of permuting N identical particles when summing over microstates. Yet, there existsome mixing scenarios for which the expected thermodynamic outcome depends on the viewpointone chooses to justify this combinatorial term. After a brief summary on Gibbs' paradox and what isthe standard rationale used to justify its resolution, we will allow ourself to question from a historicalstandpoint 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 itsresolution. We will then turn to the statistical thermodynamics of discrete and continuous mixturesand introduce the notion of composition entropy to characterise these systems. This will enable us toaddress, 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 ofthe Landauer bound regarding the minimum amount of heat to be dissipated to reset one bit ofmemory.</p>