That's a really profound question that deserves serious research, IMO. Communication is easy enough to define using Shannon's theory of information. I would argue that computation is subset of communication: signals go in one end of a 'processor' & come out the other (so the processor acts as a 'channel' in communication theory), but the data comes out modified in some non-trivial way, which distinguishes computation/processing of information from mere replication of the signals at the output.
A trivial modification would be something like (X,Y) -> (Y,X), just re-ordering cables. A non-trivial modification would be something like (X,Y) -> (X XOR Y, X AND Y). Both of these 'channels' have 2 bits of capacity, but intuitively only the second one is actually doing any information processing/computing.
I haven't found a satisfactory way to formalize my intuition about what is 'non-trivial' and to quantify how much 'processing' is being done by a general system, in such a way that one could meaningfully compare a brain and a CPU, for example. I think it's a great research question.