Gibbsian Ensemble: Kerson & Huang Explained

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The discussion centers on confusion regarding the Gibbsian Ensemble in Kerson and Huang's Statistical Mechanics. The author questions the interpretation of the density function, specifically \rho (p,q,t) = d^{3N}p d^{3N}q, and its implication of infinite representative points in phase space. They argue that integrating over allowed momenta and positions should yield infinity due to the infinite number of systems. However, they note that this conclusion may not hold if the volume of integration is finite or integrable. The conversation highlights the complexities of statistical mechanics and the nuances of integrating over phase space.
emob2p
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Hi,
I'm taking a course in Stat Mach using Kerson and Huang's Statistical Mechanics book. I am quite confused with their treatment of a Gibbsian Ensemble. They say imagine an infinite copies of the same system whose state can be represented by a point in phase space. Then \rho (p,q,t) = d^{3N}p d^{3N}q is the number of representative points contained in the infinitesimal volume. So if we integrate this over allowed p's and q's, we should get infinity because we started out w/ an infinite number of total systems. Can this be correct?
 
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Not if the volume of integration is finite or infinite but integrable.
 
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