The microcanonical entropy is multiply differentiable. No dinosaurs in microcanonical gravitation: No special "microcanonical phase transitions"
Gross, D. H. E.
Original · EN
The microcanonical entropy S=[W(E)] is the geometrical measure of the microscopic redundancy or ignorance about the N-body system. Even for astronomical large systems is the microcanonical entropy everywhere 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 microcanonical entropy like "microcanonical phase transitions", and exotic patterns of the 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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