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Re: Second law



Quoting Bernard Cleyet <anngeorg@PACBELL.NET>:

The second law is mathematically proved?

No.

The second law is physics, not mathematics.

Anything that can be proved is mathematics, not physics.
For example, you can prove theorems about Euclidean
geometry ... but then how do you know that the universe
is Euclidean? Hint: it isn't, not exactly.

As always, rather than asking "is XXX proved", it is better
to ask
-- How do we know XXX?
-- How sure are we of XXX?
-- How is XXX related to the other things we know?

Assumptions?

That's a much better question.

(particles observe N's laws.)

Not required. Post-Newtonian (SR and GR) behavior is no
threat to the second law. Same for QM.

Equipartition isn't necessary?

Indeed not. Assuming equipartition is tantatmount
to assuming the system has a temperature, which is
not required for the second law ...
... which is important, since not everything has a
well-defined temperature. Entropy is well defined
even when the temperature is unknown, undefinable,
irrelevant, or zero, as it says at
http://www.av8n.com/physics/thermo-laws.htm

=============

On a day-to-day basis, the second law is enforced by
conservation of phase space, i.e. Liouville's theorem.
The latter is a consequence of canonical mechanics
(Hamiltonians and Lagrangians et cetera). This
is the same mechanism that enforces the uncertainty
principle, and AFAICT anything that violated the 2nd
law would also violate the uncertainty principle.

The diagram is:
/==> second law
canonical mechanics ==> Liouville
\==> uncertainty principle

(where each implication also depends on mild side-
assumptions)

The overwhelming preponderance of the evidence is that
the universe does play by the rules of canonical
mechanics. I'm having a hard time even imagining what
form a deviation would take. Maybe if hbar was changing
as a function of time or something verrry weird like that.
It's possible, but I'd rate it about as likely as
non-conservation of electrical charge, or a breakdown of
Einstein's equivalence principle.