For those who are unfamiliar with Prakash's work... He did his PhD at MIT's Media Lab on "Microfluidic Bubble Logic", which is the earlier basis for this work. Here's his thesis (big PDF): http://cba.mit.edu/docs/theses/08.09.Prakash.pdf
Yeah I'm really trying to think. It's tough to think of something where a computer can't just process and then have some output that changes physical matter after or even during the process. So it would need to be something that requires the object that is doing the calculation to change while calculating?
Note that it was created by the same guy that gave economics the Phillips curve. And frankly the hydraulic computer was his better work.
Why it has gotten ignored is perhaps because it is inherently non-equilibrium and packed with feedback loops, both elements that are anathema to (neo-)classical economics.
If someone wants to have a look at a modern replacement, i would recommend Minsky.