the ultimate refrigerator

John K Clark (
Tue, 16 Dec 1997 23:03:18 -0800 (PST)


>Wei Dai writes:
>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.

>Robin Hanson <hanson@econ.Berkeley.EDU>
>I think this analysis is confused.

It looked right to me.

>Erasing a bit costs one bit of entropy regardless of what
>temperature you do it at.

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 the
growth of entropy, it's possible that entropy will keep on increasing forever
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.

Consider a computer with the smallest possible memory, just one bit. The
computer could be in two states, zero and one. Now record something into the
computer's memory, for example one. You have reduced the states the machine
can be in, from 2 to 1 in this case, and because the entropy of an object is
the logarithm of the number of ways the parts of an object can be rearranged
without changing its macroscopic attributes, that means you have reduced the
entropy of the machine too.

According to the second law of Thermodynamics you can locally reduce the
entropy of something but it takes energy to do it. As Wei Dai pointed out the
absolute minimum energy it takes to erase one bit of information is ln(2)kT ,
k is Boltzmann's constant 1.381 X10^-23 J/K, and T is the temperature of the
computer in degrees Kelvin. This is not a lot of energy by everyday standards,
but it is free energy that must be dissipated as heat if you want to erase
one bit of information. One solution to this problem is to keep things very
cold, a better solution is simply don't erase information.

With reversible computing, that is where the output uniquely determines the
input, nothing is erased in computation so you don't have this energy loss
and a logical operation can be performed with an amount of energy that is
arbitrarily close to zero. 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. Even a small reduction in speed can
help a lot in energy saving, the power dissipation (per unit of time) falls
as the square of the speed.

I have thought of a problem with the Black Hole refrigerator idea however.
You're going to have to put your heat radiators pretty close to the event
horizon because Black Holes are small but they must fill a large part of the
shy. When you get that close the huge gravitational field is going to blue
shift light, including the ubiquitous cosmic microwave background radiation,
except that it wouldn't be microwave radiation anymore, it will be infrared
or beyond.

John K Clark

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