Entropy

The thesis first discusses the history and general
properties of entropy, concentrating on the mathematical
properties. It then introduces the formalism of
stochastic quantum mechanics and the stochastic
Boltzmann-Gibbs-Shannon entropy, emphasizing the
advantages of the stochastic formalism. The relative
entropy for the spin 1/2 system is constructed in the
formalisms of usual quantum mechanics and stochastic
quantum mechanics. The maximum spin entropy states are
then found for the quantum mechanical relative spin
entropy and the stochastic classical relative spin
entropy. The latter is shown to be an acceptable
candidate for a new relative spin entropy for the
spin 1/2 system.

Dynamical systems research has found evidence that global properties of self-system, i.e., self-esteem (SE), self-stability (SS), and self-certainty (SC), emerge from coherence of self-relevant information. Self-certainty may play a role in self-esteem and self-stability. Traits were deconstructed into levels from extremely to not at all. Ss indicated frequencies of trait levels, completed Rosenberg SE, SS; and self-evaluations of traits, roles, certainty, and importance. Entropy H identifies meaningful distributions of deconstructed traits. H may be useful alternative to variance from the mean in identifying individuals for whom a trait is meaningful despite the high variability of endorsements. Low H indicated order. H correlated negatively with SC, SE, SS, ratings of traits, roles, and importance as predicted. SC accounted for some of the variance of the relations; SS, however, was found to play a greater role in the relations of entropy and global properties.