[Phys-L] Re: entropy: increased by stirring, decreased by observation

[John Denker <jsd@AV8N.COM>]

On 06/13/05 10:36, Fayngold, Moses wrote:
> I think the analogy between entropy and kinetic energy is
> superficial.

Call it what you like, or ignore it altogether if you don't
find it helpful.  It is
   a) just an analogy, and
   b) not the crux of my argument.

> The latter explicitly depends on speed which is a relative variable,
> determined, by definition, with respect to a certain reference
> frame.

Well, if that's how you look at it, the analogy is much
better than you think.  When we assign probability to
events in nature, all probabilities are conditional
probabilities, conditioned on the state of the observer.
As a corollary, all entropies are conditional entropies
(since entropy is defined in terms of probability).

I stand by my assertion that different observers will
assign different values to "the" entropy.

> The former (according to its thermodynamic definition dS = dQ/T)

That is *not* a suitable definition for entropy, for
several reasons.
  -- For starters, there is no such thing as dQ.  There is no
   Q that can be differentiated to yield T dS (except maybe
   in trivial cases).
   http://www.av8n.com/physics/thermo-laws.htm#sec-non-exact
  -- Also, S is well defined even in cases where T is zero,
   unknown, or undefineable.
   http://www.av8n.com/physics/thermo-laws.htm#sec-entropy

> As to a tiny fraction known by humans of an awesome amount of
> information about a macroscopic system , - what about a container
> with liquid helium in superfluid state arbitrary close to T = 0? If
> John knows its state, but Mary does not, what entropy should we
> attribute to the container?

Thermodynamics is most useful when applied to systems that are
reasonably close to ideal.  For systems that are recklessly
dissipative, the second law imposes virtually no constraints
on the system, so we are left with just the first law, and the
problem can be treated by plain dynamics (as opposed to
THERMOdynamics).

If Mary follows a strategy that is even remotely close to
ideal, the first step will be to determine whether or not
the system is in the superfluid state.  This requires only
a few bits worth of observations.  So the entropy reported
by Mary differs (in absolute terms) by not very much from
the entropy reported by John.

Again:  I stand by my assertion that the information in the
observer-system must be taken into account.  In a complete
cycle, this focusses attetion on measurement/observation
processes.  If you don't do this, you will get the wrong
answer every time when analyzing Maxwell demons, Szilard
engines, reversible computers, et cetera.
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