But they don't need to show a "qualitative" difference because intuitively there is one (or at least it seems that way ) -- our consciousness. The process is a sort of sick obsession with that old religious strawman "science says we are nothing but particles, so obviously science is wrong because clearly we can do all kinds of things that particles cannot." As with any strawman, efforts to get rid of it are resisted in full by those clinging to it.
At the root of the argument the two camps can be broken down like this:
On the one hand, the computationalists like you and I say "hey, there is no *strictly* qualitative difference, but if you have enough quantitative differences stacked on top of each other it ends up looking like a qualitative difference." And of course those stacked quantitative differences are exactly what you mentioned recently -- the information thing, the entropy thing, the computation thing, etc.
On the other hand, the anti-computationalists say "we know there is a qualitative difference -- human consciousness -- and if you can't account for that qualitative difference with science then there must be some non-science going on that is responsible for it."
Of course there are outliers like Piggy who want to be computationalists but still think there is a strictly qualitative difference, etc, but for the most part everyone falls nicely into the two above camps.
So the strategy employed by westprog for years now, and more recently by Malerin and all the other anti-computationalists who jumped on the bandwagon, is to oppose every effort we make to show any objective scientific difference at all between life, computers, and all the rest. They know from life experience (they aren't stupid, after all ) that yes, actually, stacked quantitative differences can appear qualitative and they know that every little quantitative difference science can show is just another step towards the computationalist position. Thus they fight every little step.
It becomes pretty obvious when you look at their posting history in totality: Well, computation exists in everything, so the brain isn't special in that regard. Well, even if computation is based on switching, switching occurs everywhere. No, transistors don't behave any differently than the rest of the universe. No, neurons don't exhibit any kind of special behavior compared to rocks. No, life is no different thermodynamically than anything else, all kinds of stuff decreases local entropy just like life does.
I have been part of this discussion for like 4 years now and the debate strategy has been crystal clear the whole time -- minimize objective scientific differences between people and rocks in order to make room for religious differences between people and rocks.