Re: DECW$CLOCK design flaw !

david20_at_alpha2.mdx.ac.uk
Date: 11/25/04 

Date: Thu, 25 Nov 2004 01:49:47 +0000 (UTC)

In article <b096a4ee.0411231903.1a6bcc07@posting.google.com>, spamsink2001@yahoo.com (Alan E. Feldman) writes:
>david20@alpha2.mdx.ac.uk wrote in message news:<cnvsh8$f8u$1@news.mdx.ac.uk>...
>> In article <b096a4ee.0411230727.706b33fb@posting.google.com>, spamsink2001@yahoo.com (Alan E. Feldman) writes:
>> >david20@alpha2.mdx.ac.uk wrote in message news:<cnq9mf$ih8$1@news.mdx.ac.uk>...
>> >> In article <opshrqtciyzgicya@hyrrokkin>, "Tom Linden" <tom@kednos.com> writes:
>> >> >On Fri, 19 Nov 2004 23:11:17 -0500, JF Mezei
>> >> ><jfmezei.spamnot@teksavvy.com> wrote:
>> >> >
>> >> >> "Alan E. Feldman" wrote:
>> >> Unfortunately entropy is a much misused term (rather like VMS clustering) with
>> >> at least two other popular uses.
>> >>
>> >> One is Boltzmann's statistical entropy which deals with the number of possible
>> >> states a system may evolve into. There are more disordered states than ordered
>> >> states for an ordered system to evolve into hence it is highly probable that
>> >> a system will evolve from an ordered to a disordered state. This is often
>> >> asserted as a reason for the direction of the arrow of time - however this
>> >|
>> >|
>> >> argument has problems since there are also more disordered states than
>> >> ordered states which could give rise to the original ordered state.
>> >
>> >Huh? The odds for a closed macroscopic system going to a more ordered
>> >state are essentially zero. It's like waiting for all the air in a
>> >room to collect into opposite corners of the room, say in 1 cubic
>> >meter or less at each corner. It's just not going to happen.
>> >
>>
>> It depends on the point of view.
>>
>> Take a closed system and define it's current state as ordered and all those
>> states which it might move to which are so close as to be pretty much
>> indistinguishable from it as also ordered. All other states it might move to
>> being considered disordered.
>
>I'm not sure what you're describing here. If the (macroscopic) system
>is in equilibrium, it will not evolve to a more ordered state. If it
>is not in equilibrium, it will evolve to a more disordered state and
>the entropy of the system will increase.
>
>> Then, for any reasonably large system, the number of disordered states D
>> vastly outnumbers the number of ordered states O. Hence in the standard
>> interpretation the system is more likely to move from the ordered to the
>> disordered state.
>>
>> But unless you introduce other constraints this isn't the whole story.
>> Consider the past of the system - where did the ordered state come from ?
>> The number of disordered states which can become the ordered state is exactly
>> the same in number as the set D (since each is just a state in D with the
>> velocity vectors reversed) similarly the number of ordered states which can
>> become the ordered state is exactly equal to O for the same reason.
>> Hence it is vastly more likely that the ordered state came from a preceding
>> disordered state than from a preceding ordered state ie the system moved from
>> disorder to order.
>
>This doesn't sound right to me. It's been a long time since I did
>statistical mechanics. Still, I think this is not right. There are far
>more states with the "wrong velocities" than there are with the right
>ones.

Of course their are a lot of states with the "wrong velocities".
They cannot evolve into the ordered state but each one of them corresponds
to a similar state with the velocity vectors reversed which the ordered state
itself cannot evolve into.

They are all those states which the system cannot evolve into
because of little things like conservation of energy, conservation of momentum
etc

In fact there aren't just a lot of states with the "wrong velocities" there are
an infinite number of them (since all the particles can be assigned any
velocity). But they are irrelevent since they cannot evolve into or evolve from
the ordered state.

>Also, I'm not sure you can really use velocities in this sense
>except for a dilute ideal gas, and maybe not even then. Quantum
>mechanics won't allow it, I think. And it seems to me that what you
>descirbe is a serious violation of the second law. It's like saying
>heat, of its own accord, goes from a cold object to a hot object.
>
>>
>> To change the situation you have to introduce a time dependent constraint
>> so that in the past the system was more constrained eg
>> you remove a partition so that the gas in an enclosed space can move into a
>> larger space.
>>
>> Note.
>>
>> In this situation statistical and thermodynamic entropy appear to be in
>> different places.
>>
>> In statistical entropy the entropy increases due to the vast number of new
>> states the system can occupy in the expanded volume.
>>
>> In thermodynamics the work done in removing the partition is done from outside
>> the system meaning it is no longer closed. Hence the system to be considered
>> has to include the agency removing the partition for instance a human hand.
>> The entropy increase then can be identified with the waste heat generated by
>> the muscles in that hand. No waste heat is generated by the gas molecules
>> having more space to move in.
>
>I think both entropies are the same. In classical thermo, it is only
>changes in entropy that are well defined. And it is only changes in
>the entropy that even matter. With the advent of statiscial physics
>(or statistical mechanics, if you prefer), entropy is given a precise
>equation:
>
> S = k ln (Omega)
>
>with Omega being the number of possible states. But even this lacks
>precision in the sense that we are talking about "approximate
>eigenstates". If we had an exact eigenstate in a closed system, it
>would remain in that state forever. But it does mean, IIRC, that the
>entropy goes to zero as the absolute temperature does. (Discussion of
>just what makes these approximate eigenstates valid is "beyond the
>scope of this discussion".)
>
But is the statistical entropy really the same as the thermodynamic entropy.
One says it occurs in the gas molecules the other in the waste heat generated
by human muscle.

>Anyway, the main point is that entropy is entropy.
>
That's one of my points. There are different definitions of entropy and it
is far from clear that they all refer to the same thing.

The other point being that just using statistical entropy to define an arrow
of time is problematic.

For another discussion of this see

http://plato.stanford.edu/entries/time-thermo/#2

>Regardless, you're not going to see the air in a room suddenly
>congregate into the corners of the room. The odds against it are
>fantastically high.
>

The chances of any particular distribution occuring is pretty close to zero.
There is nothing special about the four corners of the room.
Many people would be especially suprised if the winning numbers in the british
lottery were 1, 2, 3 ,4 , 5 , 6 . However that combination is no more or less
likely than any other lottery number combination. The greatest likelyhood is
whatever numbers you picked you would not pick the right numbers.
Similarly whatever particular spacial distribution of the air molecules you
picked would be extremely unlikely to occur eg split the room into small equal
volumes the total number of which is equal to the number of air molecules and
then specify for each volume how many air molecules it contains (0, 1, 2 etc)
(each such volume must be able to contain more than one air molecule since
it is possible for all the air to gather in the four corners of the room).
The chances of that configuration actually occuring would be similar to that
for the air to pool in the four room corners.

 
 
 
David Webb
Security Team Leader
CCSS
Middlesex University
 

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