Sommerfeld called the first part of the second law to be the entropy axiom, which is about the existence of the state function entropy. It was usually thought that the second part of the second law, which is about the non-decreasing nature of entropy
of thermally isolated systems, did not follow from the first part. In this note, we point out the surprise that the first part in fact implies the second part.
This is a brief note discussing the energy dependence of superluminal neutrino velocities recently claimed by OPERA [1,2]. The analysis is based on the data provided there on this issue, as well as on consistency with neutrino data from SN1987a as re
corded by the Kamioka detector [3]. It is seen that it is quite difficult to reconcile OPERA with SN1987a. The so called Coleman- Glashow dispersion relations do not do that well, if applied at all neutrino energies. The so called quantum gravity inspired dispersion relations perform far worse. Near OPERA energies both an energy-independent velocity, as well as a linear energy dependence with an offset that is comparable in value to the observed {delta}v by OPERA at 28.1 GeV works very well. Our analysis shows that precision arrival time data from SN1987a still allow for superluminal behaviour for supernova neutrinos. A smooth interpolation is given that reconciles OPERA and SN1987a quite well. It suggests a fourth power energy dependence for {delta}v of supernova neutrinos. This behaviour is insensitive to whether the velocities are energy-independent, or linearly dependent on energy, near OPERA scale of energies. Suggestions are made for experimental checks for these relations.
