Is the human brain more power efficient than a chess engine?\

The human brain consumes about 20W of power. Can a grandmaster win a game vs a chess software restricted to consuming just 20W (say on an iPhone, but the chess app must use only the iPhone's CPU and not rely on data sent to an external server)?

We know a mainframe can beat a GM, a PC loaded with a modern engine could give him a tough fight, but we don't know much about phone-hostile chess because no GM wants to be the first to lose to one in public.  You asked an interesting question, and my guess is that the engine is more power efficient; the engine is programmed to just do chess, the brain is also thinking about finding food and sex, and the engine can be cooled to very low temps where there's greater power efficiency, but the brain is stuck around 98.6 F.   

A decent PC loaded with a modern engine would also easily destroy most GMs. Phones are a different issue though. 

Yes but most decent PCs draw way more than 20W. IPhones must draw somewhere around 10W. It would be interesting to have a man vs machine match where the chess engine can only draw as much power as the typical human brain

Another variable to consider is the power vs. time.  As an illustration, a 100W bulb consumes 100W.  But leave the bulb on for 10 hours and it consumes 1KWh (100W x 10h = 1000W or 1KW).  so if the computer can do all the possible moves in a very short period of time, and the GM takes considerably longer, then the power efficiency of the computer moves closer to that of the GM's brain.  Of course, for this tangential theory to be meaningful the power consumed at idle (both the computer and the GM) would have to be discounted.

Can't believe I got sucked into this thread.