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Re: Entropy and states of matter



Regarding:

Specifically, that means
that the entropy in a region X cannot decrease _except_
by entropy-flow across the boundary of region X.

Wow! "Entropy flow"!

So entropy is stuff now too?

Having the ability to flow and being 'stuff' are two *different*
things.

Being able to flow (in the way that John D. uses the idea in terms
of satisfying a differential continuity equation with or w/o a source
or sink term) only requires 4 things, and none of them necessarily
have anything to do with being any kind of 'stuff'. First, the
prospective quantity needs to be approximately infinitely divisible
in space (so that macroscopic differential relationships can apply
to macroscopically infinitesimal-sized regions that are themselves
effectively so large in size on a microscopic level that they are
already in the thermodynamic limit. Second, the quantity needs to
be *extensive* at the level of the macroscopically infinitesimal
regions defined in the first point. Third, the value of the quantity
has to be able to change from place to place from time to time. And
the fourth condition is a locality of causation condition. I.e. any
changes that happen in the local value of the quantity in some
infinitesimal region of space need to be determined solely by the
conditions in that region and on the immediately adjacent regions
bounding that region via some sort of short ranged interactions that
reach across the boundaries of the local region to the immediately
neighboring regions.

When these conditions are met it becomes possible to define a local
density field and a local current flux field for the quantity. Any
quantity that satisfies these conditions may be said to be able to
'flow' and *how* it flows is described in terms of a local continuity
equation (possibly with a source or sink term). *If*, in addition,
the quantity also is a *conserved* quantity, then its continuity
equation has *no* sources nor sinks. In this latter case the only
way the quantity can change in some region is for it to 'flow' into
or out of the region across the region's boundaries (separating the
region from its surroundings). All that this 'flow' process really
means in practice is that the rate of change of the total amount of
the quantity in the region of interest is the net current of that
quantity across the boundaries of the region into the region. There
is not necessarily supposed to be some sort of connotation of the
quantity being actual ontological 'stuff'. Some of the kinds of
quantities that satisfy the above conditions and can be said to flow
are energy, entropy, mass, momentum, angular momentum, strangeness,
electric charge, hypercharge, probability, etc. (as well as numbers
of atoms or other particles of so-called 'stuff').

David Bowman
David_Bowman@georgetowncollege.edu