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(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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