the ultimate refrigerator

Robin Hanson (hanson@econ.Berkeley.EDU)
Fri, 19 Dec 1997 11:57:33 -0800

Wei Dai wrote:
>Advanced civilizations probably have extensive cooling needs. ...
>However, even at the cosmic background temperature of T=3K, erasing a bit
>still costs a minimum of k*T*ln 2 = 2.87e-23 J. What is needed is a way to
>efficiently cool a system down to near absolute zero. I think the only way
>to do it is with black holes. ...

I replied:
>I think this analysis is confused. Erasing a bit costs one bit of entropy
>regardless of what temperature you do it at. ... Negentropy is the real
>resource ...

Wei then asked:
>Would you please explain?

John Clark also responded:
>I don't know what you mean by the "cost" of entropy. Entropy is free, energy
>is not, because energy is conserved, entropy is not. I don't want to stop
>growth of entropy, it's possible that entropy will keep on increasing
>and I certainly hope it does because the only alternative is the heat death
>of the universe. Free energy is related to entropy but if the universe is
>open then it's energy any intelligence must be very stingy with if it wants
>to survive for long.
>With reversible computing, ... Landauer, Bennett and Merkle have shown that
>the amount of energy needed to make a calculation can be made arbitrarily
>small by slowing down the calculation a little.

Wei posed the problem of cooling to get rid of excess local heat, by making
contact with distant sources of negentropy (= max sys entropy - actual
such as the cosmic background. For this problem, the conservation of energy
constraint is much less important than the constraint that total entropy
decrease. In making my contribution to reversible computing
( I learned enough say with great
confidence that there is no particular advantage to erasing bits at lower
temperatures. If it were otherwise you could make a perpetual motion machine:
erase bits (= replace unknown bits with known bits) at low temps and then
reverse the operation (replace known bits with unknown bits) at high temps.
By the "costs less energy" intution this cycle would create available energy.

Robin Hanson
RWJF Health Policy Scholar, Sch. of Public Health 510-643-1884
140 Warren Hall, UC Berkeley, CA 94720-7360 FAX: 510-643-8614