It seems obvious that reversible computing is the future for Bitcoin mining ASICs, and could be the first major commercial application of the technology.
From the Reddit page you linked: "No. Hashing by definition is
irreversible and results in loss of information and therefore increased entropy."
It's irreversible because the normal circuit for SHA256d discards information (and thus requires an energy input to move in the forward direction). For example, we hash the 640 bit blockheader to get a 256 bit digest; there's no way to work backwards with only 256 bits to reconstruct the 640 bit input (the output contains less information than the input). But I don't see why there wouldn't be another circuit that performs the hash function in a reversible way, by tracking all the information that is normally discarded. This circuit would output the hash value PLUS enough of other information that one could work backwards to reconstruct the inputs.