The microcanonical entropy is multiply differentiable. No dinosaurs in microcanonical gravitation: No special "microcanonical phase transitions"

D. H. E. Gross

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The microcanonical entropy is multiply differentiable. No dinosaurs in microcanonical gravitation: No special "microcanonical phase transitions"

D. H. E. Gross

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Abstract

The microcanonical entropy $S=\ln[W(E)]$ is the {\em geometrical measure} of the microscopic redundancy or ignorance about the N-body system. {\em Even for astronomical large systems} is the microcanonical entropy everywhere {\em single valued and multiply differentiable}. Also the microcanonical temperature is at all energies single valued and differentiable. It is further shown that the recently introduced singularities of the {\em microcanonical} entropy like "microcanonical phase transitions", and exotic patterns of the {\em microcanonical} caloric curve $T(E)$ like multi-valuednes or the appearance of "dinosaur's necks" are inconsistent with Boltzmann's fundamental definition of entropy.

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D. H. E. Gross. 2004-03-23. The microcanonical entropy is multiply differentiable. No dinosaurs in microcanonical gravitation: No special "microcanonical phase transitions". https://arxiv.org/abs/cond-mat/0403582

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