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           Subject:     Crucial difference between QM and CM ?           Date: 01/31/97

'New Entropies'

On 1/31/97 MATTI PITKANEN wrote:

(MP) My definition of entropy is based on the relationship of subsystem with its complement. It is not some absolute number to be associated with closed system or to entire Universe. In this picture second law of thermodynamics is a statement about the relationship between subsystems and their complement.

(JR) I think your computer link was down when I wrote an alternative description of the Maxwell's Demon scenario. The point I was trying to make was two-fold.  First, that it is reasonable to use spatial distribution as a measure of entropy, and second, that a "single" system can have several different entropies.

My gedanken-version goes like this: Forget the Demon. We have instead 3 chambers - 2 smaller ones moving randomly inside a larger one, and an even smaller particle inside one of the smaller chambers. We set (for local purposes) the criteria that the particle can reside only inside one or the other small chambers. The "walls" of these small chambers is such that when they get
near each other, they weaken in the direction of the other chamber - basically making a hole that the particle can transit through, back and forth to either small chamber.

The "energy" of the particle never changes, just it's distribution - considered  in regard to the volumes inside the small chambers. If restricted to one   chamber, we can assign an "entropy value" to the particle. When the chambers  come to proximity and the hole gets established and the particle can now statistically be in either chamber, we can say that the entropy for the particle has increased. One of the indicators being: the statistical probability for the particle to be "in the hole" (transiting between chambers) is "greater than zero". And the "thermal-distribution" has improved (energy distribution enlarged).

In other words, we can give a QM criteria for a thermodynamic situation.

Now, however, we alter our frame-of-reference ... change the evaluation set ... and consider the "entropy" of the 2 smaller chambers vis a vis their motions within the larger Chamber. Before, they had been free-floating, also with a definable "entropy value". Now, when they are "bound" by the "greater than zero" probability for the particle re the transit-hole, the chambers are
spatially localized vis a vis each other *inside the large Chamber*, and their "entropy" *decreases* because they are more complex and localized.

A "single" event therefore contributes to changes in at least 2 separate "entropies" !! This is the foundational dynamic by which local increases in entropy at one level of constructed being *produces* (co-establishes) negentropic complexity at the next higher level of constructed being.

Does that clarify the thrust of my notions for you? Any comments on multiple-entropies?