Gibbs’ paradox according to Gibbs and slightly beyond.

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 finish 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. [ABSTRACT FROM AUTHOR]