  Polydisperse systems are commonly encountered when dealing with soft matter
in general or any non simple fluid. Yet their treatment within the framework of
statistical thermodynamics is a delicate task as the latter has been
essentially devised for simple --- non fully polydisperse --- systems. In this
paper, we address the issue of defining a non ambiguous combinatorial entropy
for these systems. We do so by focusing on the general property of extensivity
of the thermodynamic potentials and discussing a specific mixing experiment.
This leads us to introduce the new concept of composition entropy for single
phase systems that we do not assimilate to a mixing entropy. We then show that
they do not contribute to the thermodynamics of the system at fixed composition
and prescribe to substract $\ln N!$ from the free energy characterizing a
system however polydisperse it can be. We then re-derive general expressions
for the mixing entropy between any two polydisperse systems and interpret them
in term of distances between probability distributions and show that one of
these metrics relates naturally to a recent extension of Landauer's principle.
We then propose limiting expressions for the mixing entropy in the case of
mixing with equal proportion in the original compositions and finally address
the challenging problem of chemical reactions.
