Implications of Onicescu's informational energy in some fundamental physical models

Abstract

Correlating Shannon's maximum informational entropy variational principle with the constant value of Onicescu's informational energy, the uncertainty relations for canonical systems with SL(2R) invariance are obtained. The constant value of Onicescu's informational energy corresponds, through transitivity manifolds of the SL(2R) group, to the ergodic theorem and, in particular case of a linear oscillator, to a quantification condition. Specifying de Broglie's idea by a periodic field in a complex coordinate, it is proved that the oscillator synchronization group of the same ensemble is still an achievement of the SL(2R) (Barbilian's group). Integrally invoking the invariant functions through the simultaneous action of the two isomorphic SL(2R) groups, the uncertainty relations and Stoler group of synchronization among oscillators from different ensembles (i.e., the second quantification when the annihilation and creation operators refer to a linear oscillator) are obtained. Barbilian's group parameters are interpreted by means of a variational principle as field amplitudes of a stationary vacuum metric.