From owner-biophysics@net.bio.net Sat Feb 14 22:00:00 1998
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From: mmisha@nmr.mgh.harvard.edu (M. Papisov)
Newsgroups: bionet.biophysics
Subject: Re: Boltzmann's and thermodynamic entropy
Date: Fri, 13 Feb 1998 14:14:03 -0500
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In article <6c1l0r$5lm@mserv1.dl.ac.uk>, Pentcho Valev
<RUMYM@BGEARN.ACAD.BG> wrote:

The "thermodynamic enthropy" has been invented simply to acknowledge that
not all energy can be transformed into work. Nobody could explain why at
the time. Entropy was *just a member in the thermodynamic equation*. In
the simplest case (a system is being heated, there are no chemical
reactions), thermodynamic enthropy equaled to heat capacity. Anyway,
nobody knew, at the time where, the heat might go. 

In turn, the statistical explanation of enthropy was offered simply to
demonstrate where the energy actually goes, and why it can not be
completely transformed into work.

So, there is no "coincidence" or "non-coincidence": "statistical enthropy"
is simply a mechanistic explanation of thermodynamic enthropy. If you know
*exactly* how energy can be distributed between components of your system,
you can calculate a "theoretical" value that is very close to the
experimentally determined (thermodynamic) enthropy. If you don't know what
is going on in your system (like in old good days), or if the system is
too complex, you have no chance to come up with any reasinable theoretical
estimate. 

Obviously, ALL thermodynamic systems can move from a more probable to a
less probable states and back. This is what they do all the time. Lower
probability does not mean that the state is "more difficult" to reach, it
is just that you can encounter that state less frequently. If there is a
state to which a system _can not_ move, the probability of that state
would be zero.

Regards

MP

PS: Entropy has nothing to do with order. Any objections?


        > Bryant Fujimoto wrote:>>>>>>>>>
        > Nick Art <Art@EMBL-Hamburg.DE> writes:
        > >Dear All,
        > >I hope if someone could tell me the difference between
        > >the statistical entropy and thermodynamic entropy.
        > 
        > If by statistical entropy, you mean the entropy defined in
        > statistical mechanics, it is assumed that it is the same as
        > the thermodynamic entropy.  Measurements of the entropy using
        > the methods of statistical mechanics have always yielded the
        > same result as measurements using the results of
thermodynamics.<<<<<<<
        > 
        > We have already discussed that, Bryant, on a suitable model devised by
        > R. Alberty (do you remember?). We found that, in order for Boltzmann's
        > (klnW) and thermodynamic entropy to coincide, some systems must
        > SPONTANEOUSLY move from a MORE probable to a LESS probable state. So I
        > hope you would agree with the following answer: If systems can
        > spontaneously move from a more probable to a less probable
state, the two
        > entropies coincide. If not, not.
        > 
        > In my opinion, spontaneous movement from a more probable to a
less probable
        > state is a LOGICAL absurdity, but I may be wrong.
        > 
        > Best regards,
        > Pentcho

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