On 7/24/06, Russell Standish <[EMAIL PROTECTED]> wrote:
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
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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