Re: Entropy, Objectivity, and Timescales

[al clark <al@sci.nccu.edu>]

On Tue, 27 May 1997, Leigh Palmer wrote:

>  Why do you assume an isolated system?
> We are talking about entropy, an attribute of a real system. Unphysical
> assumptions do not help clarify what is a conceptual problem.

I have not been following this discussion as closely as I, probably, 
should have to put in my two cents, because it appears to me that Dan and 
Leigh are talking, somewhat, at cross purposes, but I'll do so anyway.

As I understand it the state of a truly isolated system never changes. 
The Schrodinger Equ. describes how certain measurable quantities would 
change with time in that state. (Of course, if we tried to make a 
measurement, the system would no longer be isolated.)

However, thermo. does not deal with isolated systems, but with systems 
in, at least, thermal contact with other systems and about which we have 
only, limited, knowledge of such macroscopic variables as total energy, 
volume, particle # etc. Under such circumstances we can never, even in 
principle, know how the system will evolve, even if we could, somehow, 
know it precise microstate at some point, because we don't know its 
interaction with its environment. So it could, in a finite time, reach 
any state that is consistent with the macroscopic parameters. Irreversible 
processes in some sense reduce our knowledge of a system, and in that sense, entropy can be 
can considered to be subjective.

Stat Mech associates entropy with the number or microstates that are 
consistent with the given macroscopic parameters, which is objective. Of 
course, questions of time scale, etc. do enter when dealing with real 
system, but I don't think that such questions are at the heart of the 
matter. The important point is that entropy deals with systems about 
which we have limited knowledge and which interact with other systems. 
As such, it is not as objective as the weigh of my thermo text. Then 
again, is the subjective/objective debate really helpful?

Finally, as to the size of the system, perhaps we could say that when the 
Stirling approx. for log(N!) is good enough the system is large enough.

Al