**Fabien Paillusson**

Enseignant-chercheur à l'université de Lincoln en Angleterre

"**N!, indistinguishability and entropy: the instructive case of polydisperse systems**"

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 interpretation of this combinatorial term one chooses and this is what we wish to investigate in this talk.

In the first part of the talk we will briefly introduce what the Gibbs paradox is about and what is the standard rationale used to justify its resolution. In a second part, 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. In a third part 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.