From: scerir (scerir@libero.it)
Date: Sat Jul 20 2002 - 01:33:09 MDT
Anders Sandberg:
> On average, they have no impact beside the noise: that entropy
> increases is just a consequence of that the universe is on
> average moving from a less likely state to a more likely state.
Boltzmann was very interested in the early stage of the
universe. He used to ask: Was it so tidy? Such an unlikely
state?
Actually the common formulations of the second law
of thermodynamics (the entropy of a closed system
never decreases; the entropy of a closed system
in equilibrium always takes the maximum possible
value) are in contradiction to the fact that the entropy
of a system obeying the Schroedinger equation
(with a time independent Hamiltonian) always remains
constant. (!)
By means of information theory it is possible to rephrase
the maximun entropy principle in other terms. Suppose that
for some system you know only a few macroscopic
quantities, and you have no further knowledge of it. Then
the system is expected to be in the state with maximal
entropy, beause if it were in a state with a lower entropy
it would also contain more information than previously
specified (Jaynes' principle, 1957). (However this
argument does not prove the maximum entropy principle!)
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