Re: the ultimate refrigerator

Robin Hanson (hanson@econ.Berkeley.EDU)
Tue, 16 Dec 1997 09:20:12 -0800

Wei Dai writes:
>Advanced civilizations probably have extensive cooling needs. Computing
>and communication equipment both work better at lower temperatures. A
>cooler computer means a faster computer with lower energy needs, and a
>cooler transceiver has lower thermal noise. Since these equipment cannot
>operate with perfect efficiency, they will need to eliminate waste heat.
>It's not too difficult to cool a system down to the temperature of the
>cosmic background radiation. All you need to do is build a radiator in
>interstellar space with a very large surface area, and connect it with the
>system you're trying to cool with some high thermal-conductance material.
>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. ...
>If you build an insulating shell outside the event horizon
>of a black hole, everything inside the shell would eventually cool down to
>the temperature of the black hole

I think this analysis is confused. Erasing a bit costs one bit of entropy
regardless of what temperature you do it at. It might cost less free energy,
but free energy costs more per unit entropy at low temperatures. Negentropy
is the real resource; not free energy.

Advanced civs would want to use black holes though, as they are by far the
largest source of negentropy. The entropy of a black hole goes as the square
of the mass, while the entropy is linear for more familiar uses of mass.
The big problem is that at their low temps radiation flow is very low, so
it seems a very slow process to get negentropy out of the hole by sending
radiation in.

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