r6 and I discuss his theory that entropy is subjective

[gustavolacerda]

r6 and I discuss his theory that entropy is subjective

I've never been satisfied with the solutions I've seen to Maxwell's Demon.
I take r6's interpretation of entropy as an agent-dependent quantity related to his knowledge, and a measurement of what one can do with this knowledge: knowledge is power. According to his theory, an all-knowing being (

Comments

[spoonless]

Some physicists used to toy with the notion that entropy is subjective and only refers to our "lack of knowledge" about a system. But from what I understand, computer simulations put and end to that way of thinking. Once it became possible to simulate a large number of interacting objects bouncing around exchanging energy, it became obvious that the entropy of a system is an objective quantity which refers to how many accessible states there are in the system

[gustavolacerda]

I think the answer might be that in order to compute what's going to happen in the future for a complicated chaotic system you need to do a computation which increases entropy somehow.

hm... I don't know much about reversible computation, but I argued above that you should be able to simulate the system forwards or backwards in time without erasing information, and without needing more memory.

It would be interesting if computation were under the same constraints as the physical system it simulates (e.g. if your computer contained a physical copy of the system it simulates), and irreversible computations corresponded to irreversible changes in the sytem (i.e. entropy increasing).

[spoonless]

It would be interesting if computation were under the same constraints as the physical system it simulates (e.g. if your computer contained a physical copy of the system it simulates), and irreversible computations corresponded to irreversible changes in the sytem (i.e. entropy increasing).

Yes, that's what I'm saying is probably the case. But I don't know for sure, and the situation becomes more difficult when you ask the question of how quantum mechanics fits into the whole thing.

I have a pet "hypthesis" that in the many-worlds interpretation of quantum mechanics (the interpretation which I believe in) the total entropy in the multiverse should be constant (since everything is both reversible and non-chaotic). So far I haven't seen anyone addressing this question, but I plan on investigating it at some point if it hasn't already been dealt with. I wouldn't be too surprised either way, but I would really like to know the answer to this question.

[darius]

That sounds like how Toffoli and Margolus put it (in Cellular Automata Machines -- that information is conserved and that's why we have thermodynamics. (I'm paraphrasing.) (Your point about the multiverse is something I've wondered about in this connection -- information doesn't seem to be conserved in the particular branch we're on after a measurement.)

[spoonless]

Wow, I'm surprised they mention that in a cellular automata book. I know Toffoli has done important work in quantum computing, though, which is somewhat closely tied to the modern many-worlds revival. I might be curious enough to pick up that book

[darius]

I wish I had the book ready-to-hand to relay it more accurately. It was a few remarks in the chapter on reversible CA, IIRC -- it left me wishing they'd spell it out more

[spoonless]

My take on it was, information from a god's-eye point of view is conserved: a 1-to-1 local update function in a CA, symplectic flows in classical mechanics, unitarity in quantum mechanics. But if you a flip a single bit in a reversible CA that's at all interesting, the trajectory rapidly diverges, and 'therefore' any imperfection in an agent within the system causes it to lose accurate information in its representation -- so the god's-eye conservation of information along with the interestingness of the dynamics means that agent's-eye information can decrease but not increase. (It can try to dump the lost information into parts of the system state it's not interested in, though.)
Yes, that's exactly how it works. From the point of view of any observer in quantum mecahnics, information is always being destroyed. That's one of the main things I like the many-worlds-interpretation. It is the only interpretation where you can have a God's-eye view of the system where information is conserved. The illusion of the destruction of

[darius]

Toffoli was into reversible computing before anyone thought of quantum computing. The action paper is "Action, or the fungibility of computation" at http://pm1.bu.edu/~tt/publ.html -- if you take a look and can figure out what he's talking about, I'd like to hear it. :-) (I could probably work it out myself but it was too much effort to bother.)

I'd be interested in your thoughts on reversibility and information if you get around to them.

[darius]

I think your question is subtly different from Maxwell's Demon, who is supposed to extract useful work from the system, e.g. by pushing a piston against an external resistance. We can imagine two different idealizations of that interaction with the outside: either the demon has perfect knowledge/control of it -- it's microscopically reversible to the demon -- or it's a random interaction with a heat bath at some temperature. In the first case, to keep doing additional useful work we need an endless supply of zero-entropy resistance -- the demon must have an endless supply of prior information. In the second case, at the end of an expansion the demon no longer knows the exact state of the insides -- which I wrote about before

[spoonless]

darius has it exactly. In order to move one ball into a specified place you at least have to gain knowledge of that ball. The only option after that is to erase that knowledge or keep it. If you erase it, you must dissipate heat because that's an irreversible process. If you don't erase it than you end up needing a lot of storage in the long run.

[gustavolacerda]

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