Posted by
Robert Holmes on
Jul 25, 2006; 3:38am
URL: http://friam.383.s1.nabble.com/Definition-of-Complexity-tp522229p522251.html
On 7/24/06, Russell Standish <r.standish at unsw.edu.au> wrote:
>
> On Mon, Jul 24, 2006 at 06:38:49AM -0600, Robert Holmes wrote:
> > Interesting paper Russell but I don't think I get it yet. Could you
> clarify
> > why entropy is emergent under your definition (" An emergent phenomenon
> is
> > simply one that is described by atomic concepts available in the
> > macrolanguage, but cannot be so described in the microlanguage")?
>
>
> Entropy is give by the Boltzmann-Gibbs formula once the thermodynamic
> state variables are fixed (total energy, pressure, temperature and so
> on). Nothing in the microscopic description of matter says these are
> the relevant state variables.
Still don't get it. I suppose it depends on what you mean by "nothing in
the microscopic description says these are the relevant state variables". If
this means that Boltzmann's postulate S = k.ln(omega) doesn't explicitly
contain U, F, etc. then you are right. But actually I don't need many more
equations to derive precise equations for U and F. Specifically, all I need
is dU = dQ + dW and dQ = TdS and after a page or two of math I've got
equations for U, S and F in terms of the partition function (see for example
Glazer & Wark, "Statistical Mechanics: A Survival Guide"). So I don't quite
see how you can say that the microscopic description doesn't tell us about
the macro description. As G & W put it: "if we know the partition function
for a particular system we then know all of the thermodynamic functions. It
is difficult to overstress the importance of this."
What am I missing?
Robert
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