Oh sorry! Yes, I see now that you did label extensive and intensive, missed that the first time I looked at it.
Extensive means the same thing for any quantity. So if you change it for entropy, yes it should be changed for all. I’m not sure what the simplest least misleading way is to state what extensiveness is — perhaps that’s why it’s a word in itself :-)
The basic intuition behind extensiveness is just that certain properties of a system grow in a linear way when you make a bigger version of the same system. But since there are multiple ways of imagining what bigger means, you just have to be careful. Simply giving something more space to move around in is not making the system bigger — scaling it up while keeping the density the same is more what someone should have in mind when thinking of “extensiveness”.
As long as you’re imagining the right kind of scaling up, then volume can be a good proxy for system size. But it’s more the size of the system that’s fundamental to what extensiveness is.
