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 | | From: | transformer | | Subject: | Entropy model discredited | | Date: | 22 Jan 2005 11:02:59 -0800 |
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 | Dear All,
I just read Jozsef Garai's work: Entropy is a Mathematical Formula.
It's here:
http://www.fiu.edu/~jgara002/research%20statement/Entropy/Entropy.htm.
The article states that the microscopic explanation of entropy has
been challenged from both experimental and theoretical point of view.
If Boltzman's formula is not adequate to explain entropy is Shannons?
Is Nature acting different than Information Theory entropy wise? The
article says Boltzman's entropy model has exceptions,what about
Shannons model?
I'm confused, has anyone else developed an alternative model?
Thanks
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| | From: | Willem | | Subject: | Re: Entropy model discredited | | Date: | Sat, 22 Jan 2005 21:25:57 +0000 (UTC) |
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| transformer wrote:
) Dear All,
)
) I just read Jozsef Garai's work: Entropy is a Mathematical Formula.
) It's here:
) http://www.fiu.edu/~jgara002/research%20statement/Entropy/Entropy.htm.
)
) The article states that the microscopic explanation of entropy has
) been challenged from both experimental and theoretical point of view.
)
) If Boltzman's formula is not adequate to explain entropy is Shannons?
'entropy' in Shannon isn't the same as 'entropy' in Thermodynamics.
Therefore you cannot draw such analogies.
HTH, HAND.
SaSW, Willem
--
Disclaimer: I am in no way responsible for any of the statements
made in the above text. For all I know I might be
drugged or something..
No I'm not paranoid. You all think I'm paranoid, don't you !
#EOT
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| | From: | Matt Mahoney | | Subject: | Re: Entropy model discredited | | Date: | 22 Jan 2005 16:11:00 -0800 |
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| Willem wrote:
> transformer wrote:
> ) Dear All,
> )
> ) I just read Jozsef Garai's work: Entropy is a Mathematical Formula.
> ) It's here:
> )
http://www.fiu.edu/~jgara002/research%20statement/Entropy/Entropy.htm.
> )
> ) The article states that the microscopic explanation of entropy has
> ) been challenged from both experimental and theoretical point of
view.
> )
> ) If Boltzman's formula is not adequate to explain entropy is
Shannons?
The paper states that the second law of thermodynamics can be derived
from the first law. I don' see how this is in conflict with the
interpretation that entropy is a measure of the uncertainty of a
system's state.
The auther cites examples: the spontaneous crystallization of
supercooled liquids and supersaturated solutions. These do not violate
thermodynamics because such reactions give off heat. Also the
transition between solid helium and superfluid helium II (which has
zero viscosity) is not in conflict. Superfluid helium is an ordered
state, like a crystalline solid. It is fluid because the atoms exist
in a single quantum state, like the atoms in a Bose-Einstein condensate
or the electrons in a superconductor.
One problem with the interpretation of entropy as uncertainty of the
microstate given the macrostate is that in order for this definition to
work, the macrostate can only be approximately known. In practice we
do not know the energy or temperature of a system with infinite
precision. The author argues with an example of 4 particles and 6
energy levels, which is flawed for this reason. If the energy levels
were slightly different from each other, then knowing the energy
exactly would imply complete knowledge of the microstate, or entropy =
0.
> 'entropy' in Shannon isn't the same as 'entropy' in Thermodynamics.
> Therefore you cannot draw such analogies.
I think they are. They both measure uncertainty with respect to an
observer, which is a finite deterministic state machine (whether it is
implemented in silicon or neurons). This has an important implication.
Thermodynamics requires that the entropy of a system increase over
time. However the entropy (in the information theoretic sense) of a
state machine in the absence of input decreases over time. This
implies that computation requires energy, and sets a lower bound.
-- Matt Mahoney
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