Although the Gamma distribution is known within statistical mechanics to describe the probability that a classical ideal gas at a fixed temperature occupies a given energy state it appears to have been all but forgotten. In this paper we present a new and much simpler derivation starting from the Maxwellian velocity distribution. The analysis is extended to open systems in which the number of particles fluctuates. Computer simulations using a hard‐sphere model of a classical ideal gas are used to support the theoretical considerations and show how the Gamma distribution applies in practice. The resulting probability distributions are used to calculate the Shannon information entropy which is then compared with the thermodynamic entropy. We point out an important proof in information entropy that also appears to have been overlooked in statistical thermodynamics and argue on the basis of the work presented here that information theoretic entropy and thermodynamic entropy, whilst obviously related, are not necessarily identical.
Dr. Charles Kenneth Thornhill, who died recently, was a proud, gritty Yorkshireman who, throughout his long life, genuinely remained true to himself. This led him into conflicts within the scientific community. The jury is still out on whether he was correct or not in his ideas but, be that as it may, all can learn a tremendous amount from the courage of this man in standing up for what he truly believed.
The alleged existence of so-called Planck particles is examined. The various methods for deriving the properties of these ?particles? are examined and it is shown that their existence as genuine physical particles is based on a number of conceptual flaws which serve to render the concept invalid.
The new mathematics, referred to as iso-mathematics and geno-mathematics, introduced by Santilli to help explain a number of outstanding problems in quantum chemistry as well as in other areas of science such as astrophysics, has been applied successfully in a number of physical situations. This new formalism has, for the first time, provided an irreversible description of thermodynamics via an irreversible differential calculus together with the related mathematics. However, the associated thermodynamics has not been considered so far. That defect is remedied here.
It is pointed out that the usual derivation of the well-known Maxwell electromagnetic equations holds only for a medium at rest. A way in which the equations may be modified for the case when the mean flow of the medium is steady and uniform is proposed. The implication of this for the problem of the origin of planetary magnetic fields is discussed.
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.