Re: Entropy classical only?

On Mar 20, 6:55 pm, "galathaea" <galath...@xxxxxxxxx> wrote:
On Mar 20, 11:51 am, "rayoha...@xxxxxxxxxxxx" <juanp...@xxxxxxxxx>
wrote:



On Mar 19, 8:52 pm, "rayoha...@xxxxxxxxxxxx" <juanp...@xxxxxxxxx>
wrote:

On Mar 19, 3:48 pm, "Autymn D. C." <lysde...@xxxxxxxxxxxxx> wrote:

On Mar 19, 4:11 am, "rayoha...@xxxxxxxxxxxx" <juanp...@xxxxxxxxx>
wrote:

galathea ... may be we are talking in the same way ... I must to study
carefully your considerations ... I must to read about H-theorem and

-to
-to
must is not reflexive.

I was not carefully in develpping my observations ... so if I´m wrong

careful
developere

the central point that I want to remark in the simple example that I
give above is
that correlations exists so time symmetry doesn't dissapear ... but
its contribution are of null measure

this is because in the case of ergodic chaos most of the trayectories
in both directions after an enough
time (times goes to infinity) increases entrophy ... here the
exeptions are of null measure

from the birkhoff's theorementropyin microcanonical ensemble are
maximized ... because
the density state rho becomes constant in phase space ... so from an
arbitrary initial condition
in the example systemonlythose with null measure doesn't follow
ergodicity ...so most of the
intial conditions ... including reverse times ones follows ergodicity
and maximizesentropy... in
factentropydoes not grows, it just remains at its maximum value

here arbitrary initial conditions must be interpreted as that rho is
constant from the start ... from
Lliuville's theorem ... rho must remaing constant in time in the
closed system

so ... pick an arbitrary initial condition drawn from rho =
contant ... then evolve the system
trough infinite time ... then it must follow from Birkhoff's theorem
thatsentropyreaches its
maximum value ...

ok ... now I'm conscious about the fluctuation theorem ... here the
paradox reamins unsolved ...

I think that in the example that I give above ... the system start
from equilibrium ... so from Lliuviles theorem
,from the hypothesis of being an isolated system and from the
hypotesis of ergodicity, then the system remains
over all time in equilibrium ...

but ... what happens if the system starts far from equilibrium ?? ...
from boltzman ... then the system relaxes to equilibrium ...
but then Lodschimtd's paradox appears ... for to bolztamnn holds ...
it requires molecular chaos ... but this is inconsisten with
the assumption of an time reversible isolated system ...

that is the point where the switch occurs
in most "derivations" of the second law

multi-particle statistics get substituted for dynamic evolution

obviously ... this is not a problem for the canonical ensamble where
the system it's not isolated ... there the information production
of the heat reservoir sends the system just to the equilibrium macro-
state

so I think ... that galatea it's right ... mechanical statistics
principles holds if you consideronlya very small part of the
universe as the system ...
in fact ... I'll found a quantum analogs of these results ... and in
it ... theentropyof the universe its 0 ... but that of the system
its the maximum admited
by the constraints ... in fact all the universe in this paper is
considered deterministic ... but by means of entaglement between the
system and the remaining part of the universe the information leaks
into the system pushing it too the thermodinamic equilribrium state

but even here the problem cannot be assumed to go away
until theentropygets properly tied to energetics

all the "proofs" of the second law i have seen which use entanglement
either work towards the association of informaticentropy
(von neumann, kolmogorv, etc.)
or extend quantum mechanical laws to make the energetic association

there does not appear to be a natural association
and a number of papers illustrating violations of clausius' inequality
in integrable two-state quantum systems
seem to bear this out

to make this even clearer
entanglement does not seem to have the properties
necessary to cause a column of gas to equilibriate in temperature

a natural stratification in the direction of gravity occurs
whenever the carrier of the heat is affected by gravity
(eg. has mass or energy density)

this makes sense even in theclassicalexplanation
because particles that have moved down the column closer to the bottom
have accelerated
those that have moved toward the top have slowed

however
if we were to follow through the derivation of boltzmann's h-theorem
the energetics relevant to position in the gravitational potential
gets lost

the derivation implies the energetic result of the second law
by allowing statistics to "forget" distinctions of position
and mix particles at different strata

this has no knownclassicalor quantum explanation

this type of mixing is a new phenomena
distinct fromclassicalor quantum ensemble flows and statistics

however
revisions of szilard's idea _are_ able to connect informatics with
energetics
when the interaction is a pointlike decision process
or when environmental interactions cause perturbative mixing

but the top and bottom temperatures in the gas column
can be made to differ by arbitrary deltas
and perturbing the paths of evolution of the constituent particles
cannot "boost" the energies by an arbitrary amount

over the past few months
i have come to suspect very strongly that this difference is
fundamental
and not simply a missing influence

that fields
due to their interactions being over distances
and not pointlike like szilard
violate any attempt at recovering the szilard mechanism

this includes path perturbation methods
fluctuation methods
entanglement methods
and many other "local mixing" methods

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar


ok ... try to read the following paper ... nature physics vol. 2 no.
11 november 2006, Entanglement and the foundations of statistical
mechanics, Sandu Popescu, Anthony J. Short and Andreas Winter.

there is an intereseting aproach where entanglement leads to
maximization of Newmann entrophy, altought it has some questionable
points, as for example the finite dimensionality of the Hilbert
spaces, and the not enough justified particular choice of the
distance between quantum densities, but I think that the idea behind
its interesting ... and in the future (may be) it can be
generalizated.

best regards

juan.


.

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