Is Entropy a "property" or a "primrose-path"?

[Bill Eshleman]

Dear Gyula,
You responded to the concept of “Entropy and the H-theorem”
with this excellent argument.

“At the connection of Entropy and H-Theorem some basic assumption are not correct:

– First of all: the positions, x, and the velocities, v, are not intrinsic properties of particles.
– x and v are never known exactly: definite initial conditions, definite assumptions about x(t), v(t) at some time exact t is impossible.
– The infinity (infinite large and infinite small) distances belong not to physical descriptions. The particles cannot be too close to each other.
– Intrinsic properties of particles are two kinds of conserved charges qi and gi,; they are elementary electric and elementary gravitational charges.
– qi and gi generate two fundamental interactions; the interactions are non-conservative in presence of charges. The interactions propagate with c. The interactions between particles can be attractive or repulsive.
– Never exist particles without charges; never exist particles without interactions.
– In small distances the electromagnetic interaction dominates. In large distance the gravity dominates, however, electromagnetism is also always present.
– Elastic scattering of particles can never occur. The particles are always correlated.
– Particles and fields appear always together.
– What is the equilibrium of matter composed of particles and fields? Is the equilibrium the state of neutrinos or the neutron stars? Or somewhat other?

Almost each basic assumption at the foundation of entropy is incorrect.”

But I’m thinking that you demand too much from the concept
of Entropy by wanting it to have “first-principles” when
the possibility exists that Entropy is itself, a “first-
principle”, needing no further assumptions at all.

It is hard for me to put into words, but suppose that what
looks to you as “invalid assumptions” are really just
approximate implications of the concept of Entropy;
conclusions which are themselves uncertain and seemingly
disordered. Boltzmann’s “thermodynamic entropy” seems of
little use, but when it got “cleaned-up” when analyzed by
Gibbs and statistical mechanics and finally Claude Shannon,
reality has become a “mixture-problem” much like bags of
Jelly-Beans in a Jelly-Bean candy store, where the licorice
flavors (positrons and eltons) are almost anomalous and in
which measurements can never be exactly determined.

If anything is to be assumed to be “exact”, I hope it
is that Entropy is the only conserved property of open-
systems among a multitude of breakable symmetries.

That force, momentum, and energy(among other things) are NOT conserved, and that Entropy is the only conserved
property of interactions.

I even question the appropriateness of thinking that 23,000
year old data about orbits near spiral galaxy cores predicts
what the cores are now; that is, if our Milky-Way’s core
imploded into a parallel universe today, that we would not know it until 23,000 years from today; and that year 25,016
astronomers would be pondering this “dark” gravitational
force with no apparent source; a source which may have
existed long ago, but is now somewhere else; a symmetry
which seems to violate conservation of information, but
does not.

Sincerely,
Bill Eshleman

[Gyula Szász]

“If anything is to be assumed to be “exact”, I hope it is that Entropy is the only conserved property of open-systems among a multitude of breakable symmetries.
That force, momentum, and energy (among other things) are NOT conserved, and that Entropy is the only conserved property of interactions.”

The only conserved properties of interactions are their sources and their constant propagation c.

[Bill Eshleman]

Dear Gyula,

You said:
“The only conserved properties of interactions are their sources and their constant propagation c.”

I must agree, but then I must conclude that it is really
the entropy which is conserved and propagated at c…….

So in this fashion, Atoms and Entropy would be equivalent
notions and this is what I’m thinking Boltzmann
was “getting-at” in the first place. That is, that conserved particles and conserved waves are what might be
called “entropy-packets”(-P times Log(P)) and symmetric in
Nature.

Sincerely,
Bill Eshleman

[Gyula Szász]

“.. it is really the entropy which is conserved and propagated at c…….”

Unfortunately, not! The interactions propagate with c and the sources of the interactions are conserved

[Bill Eshleman]

This Wikipedia entry is what I was exposed to at university;
it was called Communication Theory at that time. The so-
called “other” entropies still baffle me. I call it the
“candy-store” entropy and have been utterly brainwashed and
hung out to dry, on its “truth”.

https://en.wikipedia.org/wiki/Entropy_(information_theory)#Entropy_as_information_content

Communications require a transmitter, a channel, and a receiver. This theory allows electrical engineers to
describe the information content of alphabetic characters
and words so that optimal(but noisy) channels can be
determined.

e, P, p, E is the alphabet, the atoms and composite
particles are the words, the radiations are the noise,
and the channel is space(time).

To me, the analogy is fascinating; so I think/speculate
that most, if not all, models of particles and their interactions can be modeled not necessarily with Newton’s
old-style Calculus, but with the more modern Shannon
Information(communication) Theory concepts instead.

But it is important to know that I view this as merely an
hypothesis; the theory comes to me courtesy of Boltzmann, Gibbs, et. al., and finally Shannon.

Entropy is an extensive property and its paths are real
and reversible and conserved and symmetric(usually).

Thank you, cough, cough.

[Bill Eshleman]

And this is the man who might be responsible for
creating a new way to replace Calculus as a modeling
language. He got the 2009 Fields Medal for studying
the Boltzmann Equation.

[Gyula Szász]

The distinction between my effort and what Boltzmann, Gibbs, et. al., and finally Shannon done is that I have a dynamical proposal for several concrete particles with concrete fundamental interactions.
This is a completely other purpose as Boltzmann and the other have had modeling.

[Bill Eshleman]

A suspicious dichotomy, I’m thinking. A hidden symmetry.
Possibly even a symmetry between Calculus and Information
Theory. Or maybe even as “trivial” as “d” versus “delta”,
and “integral” versus “summation”. To my way of thinking,
numbers are only numbers, so maybe the symmetry is between
the “concreteness of reality” and the “nothingness of
numbers”…….

[Bill Eshleman]

I’m even thinking that Feynman diagrams could easily
have been developed as “entropic” instead of “energetic”
He sums vectors that occur simultaneously, and dot products
vectors that occur one after the other. I like Feynman diagrams, but sadly, they only represent how shallow my
understanding of QM is. 🙁

[Bill Eshleman]

And that minus-sign that you modern physicists put into my
“precious” Pythagorean-Theorem; I don’t interpret what
happens as the creation of an imaginary axis; I see it as
the creation and/or revelation of another real 3-dimensional
world for so-called “weak-fields”; a world where our copies
see time as the cause of interactions, whereas in this
world we see the opposite…. that interactions are the cause of time. And as the fields get stronger and
stronger, more and more other worlds get created and/or
revealed.

That the “weak-field” “other-world” could be an (E, p)
world, would be very elegant indeed.

The irony might be that for the “strong-field” we may
be detecting particles that belong in the other-worlds and
not in this world at all.

[Bill Eshleman]

Dear Gyula,

Now, with my feet again firmly attached to the Earth, and
not at all attacking your theory, nor even proposing to fool
you into a chain of reasoning that could negate your
assumptions….

I propose that your theory be left intact, and suggest that
it is only the form of your formalism, your purely Calculus
treatment of motion that could stand a more statistical
flavor. When I listen to you say that the positions and
velocities cannot be determined and that the Laws of Nature
are non-deterministic but causal, I see the need for your
concept of motion to be augmented by the concept of “optimal
transport” of information(-entropy). I believe that
statistical laws are what Nature has; probabilities and
their flow is a start, but large collections of objects
need the concept of a “measure” and that the term “entropy”
is that measure. Here is another video that I think you
should be interested in:

I suggest that your formal treatment is most accurately
described as “analytic” and that Information Theory is
as Cedric says, “synthetic” and so general that elegant and
beautiful concepts are born-out-of this generality.

Sincerely,
Bill Eshleman

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