From: Mitchell Porter (mitchtemporarily@hotmail.com)
Date: Sun Nov 26 2000 - 08:24:30 MST
(The original post was cc:ed to extropians, so this one
is going there too.)
Eliezer described three ways of throwing away entropy - an
enabling technology for perpetual motion, since this would suck
some energy back from thermal equilibrium. It was just a long
detour in his post, but I want to correct some mistakes, and
make some simple comments. The issues involved are quite subtle
in my opinion, so I'll probably make mistakes of my own, but
better to mail now than wait until morning.
First, the mistakes:
>The first law of thermodynamics states that "You can't win"; you cannot
>decrease the amount of entropy in the Universe.
This is the second law. The first law is conservation of energy.
And: Hamiltonian != phase space. The Hamiltonian is a function
on phase space, whose value is the total energy, and in terms
of which you can write Hamilton's version of the laws of motion.
Now, some more substantive comments.
- The negative-energy PMM
Paul Davies talks about negative-energy perpetual motion
machines at http://www.newscientist.com/ns/980321/features.html,
along with the extra influences that would stop them working.
I would take issue with the description of phase space
here. Suppose you have a world in which particles can be
created and destroyed. This doesn't mean that phase
space changes in size each time that happens, it means that
phase space is the union of zero-particle phase space,
one-particle phase space, two-particle phase space, etc.;
and when a particle is created, you move from the N-particle
region to the (N+1)-particle region.
- The quantum collapse PMM
The proposal here is pretty vague. It's just, 'what if
entropy-increasing processes somehow acquired very low
probability'.
There is a 'quantum thermodynamics', it's called statistical
mechanics, and entropy still increases there. There's interesting
recent work in quantum information theory which suggests that
entropy and entanglement are related, and maybe there will be
distinctively quantum ways to *locally* decrease entropy ... but
there's no inkling of a global violation of the second law.
Once again on phase space ... You can conceive of a
quantum state as a wavefunction on a classical state space,
or as a point in Hilbert space, but in neither case does
'phase space'(*) itself change size when a wavefunction collapses.
In the first case, the wavefunction is suddenly restricted to
a small region of state space; in the second case, the state
vector jumps to a different point in Hilbert space.
(*) Technically, I'd rather say 'configuration space', since
phase space refers to a space which has a position *and*
a momentum coordinate for each degree of freedom, and neither
Hilbert space nor the space upon which a wavefunction is based
is like that.
- The time-travelling Maxwell's-demon PMM
This I haven't quite heard before, although I daresay someone
who studies wormholes has thought about thermodynamics in
wormhole spacetimes.
But there's a hidden energy cost in waiting for the low-entropy
states to come along. It takes energy to register the current
state and decide whether it's low entropy. So entropy will be
generated by the selection process. This is the parable of
Maxwell's demon.
As for phase space here ... the Hamiltonian framework describes
the state of the universe by a point in phase space, and the
history of the universe by a path in phase space. A universe
with time travel is probably better described in some other
way, since it likely can't be divided up into a simple series
of 'spacelike surfaces', it will have some more complicated
topology.
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