Supradegeneracy, Anti-Supradegeneracy, and the Second Law of Thermodynamics

Abstract

Supradegeneracy — degeneracy G (E) increasing with increasing energy E faster than the Boltzmann factor eE=kT decreases with increasing E — has been investigated with respect to its possibly engendering challenges to the Second Law of Thermodynamics. Supradegeneracy alone does not challenge the Second Law: if there is to be even the possibility that a system manifesting supradegeneracy can challenge the Second Law, additional requirements — over and above supradegeneracy per se — must also be fulfilled. We hypothesize what prima facie seem to be the two most obvious of these additional requirements. We then consider a simple system manifesting supradegeneracy and also fulfilling these two requirements. At least for the system that we consider, the answer seems to be negative: the Second Law seems not challenged. But I propose a simple experimental test: I hope to be proven wrong!: Only an experiment can decide the issue for sure! Understanding why the answer is at least apparently negative for the supradegenerate system that we consider may help in understanding of what at least prima facie seem to be positive results via analyses, including computer simulations but to the best knowledge of the author as of the time
of this writing not yet experimental tests, of other supradegenerate systems: of what is the minimal complete set of additional requirements — over and above supradegeneracy per se — that must be fulfilled by a supradegenerate system if it is to challenge the Second Law. Moreover, even if it turns out that all supradegenerate systems do not challenge the Second Law, they could still be useful even within its strictures. Concluding remarks are provided describing implications in general if the Second Law is violated by any means whatsoever (supradegeneracy and/or otherwise).
Keywords: degeneracy, supradegeneracy, Second Law of Thermodynamics; additional requirements, Boltzmann distribution, canonical distribution, Boltzmann factor, law of isothermal atmospheres, spontaneous momentum flow