arXiv subjects
Publications and source records attributed to J. Dunning-Davies.
Problems associated with the nonextensivity of a hadron gas were discussed some time ago. Recently the topic has come to light again and here earlier results are re-examined in the light of new knowledge and attention is drawn to problems with the more modern work.
The possibility of the phenomenon of Bose condensation having a part to play in the discussion of neutron stars has been around for some time. Here the sorts of temperatures and densities that might be involved are discussed. Also, an alternative way of viewing the Bose condensation phenomenon is examined once more and, although found to lead to more accurate results in traditional examples, is found to have little numerical effect in astrophysical examples.
Attention is drawn to the fact that the well-known expression for the red-shift of spectral lines due to a gravitational field may be derived with no recourse to the theory of general relativity. This raises grave doubts over the inclusion of the measurement of this gravitational red-shift in the list of crucial tests of the theory of general relativity.
Here the 1930's work of Milne on the relationship between the universes of relativistic cosmology and those which follow from Newtonian theory is reviewed. The extension to the case of non-zero pressure is considered also. In each case, any assumptions made are noted and the thermodynamic implications of these are explored in the final section.
For many years it was felt that, when a star collapsed, a white dwarf resulted if the mass of the original star was below the Chandrasekhar limit, a neutron star if the mass was somewhat larger but still less than four or five solar masses, but after that black holes were felt to provide the only possible final state. The extension of this hierarchy to include the possibility of quark, and even sub-quark, stars has been proposed and here is used to offer an alternative explanation for the recently published photograph, credited to Eckart and Genzel, purporting to show stars near the centre of our Galaxy moving at very high speeds. The same basic results are used also to consider the even more recent results of Schodel and collaborators concerning the detailed observations of a stellar orbit very close to the centre of our galaxy.
The derivation of Student's pdf from superstatistics is a mere coincidence due to the choice of the $χ^2$ distribution for the inverse temperature which is actually the Maxwell distribution for the speed. The difference between the estimator and the variance introduces a fluctuating temperature that is generally different than the temperature of the variance. Fluctuations in the energy of a composite system are transferred to fluctuations in the temperature via Lévy's transform. The randomization of the operational parameter leading to a subordinated process requires the same number of degrees of freedom in the directing as in the original process. In place of Student's pdf we find the subordinated process to Maxwell's speed distribution has a Pareto distribution which is interpreted as the density of the length of the random velocity vector.
Tsallis' 'statistical thermodynamic' formulation of the nonadditive entropy of degree-αis neither correct nor self-consistent.
The pseudo-additive relation that the Tsallis entropy satisfies has nothing whatsoever to do with the super- and sub- additivity properties of the entropy. The latter properties, like concavity and convexity, are couched in geometric inequalities and cannot be reduced to equalities. Rather, the pseudo-additivity relation is a functional equation that determines the functional forms of the random entropies. The Arimoto entropy satisfies a similar pseudo-additive relation and yet it is a first order homogeneous form. Hence no conclusions can be drawn on the extensive nature of the system from either the Tsallis or Arimoto entropy based on the pseudo-additive equation.
A number of elementary misconceptions on the part of the author are corrected.
There is neither motivation nor need to introduce 'superstatistics.'
The Tsallis entropy is shown to be an additive entropy of degree-q that information scientists have been using for almost forty years. Neither is it a unique solution to the nonadditive functional equation from which random entropies are derived. Notions of additivity, extensivity and homogeneity are clarified. The relation between mean code lengths in coding theory and various expressions for average entropies is discussed.