On the information and uncertainty relation of canonical quantum systems with SL(2R) invariance

By correlating the principle of Shannonʹs maximwm informational entropy with the constant value of Onicescuʹs informational energy, one can obtain the uncertainty relation for canonical systems with SL(2R) invariance. The constant value of Onicescuʹs informational energy corresponds, through transitivity manifolds of the group, to the ergodic theorem. The informational energy expression for the classical oscillator and quantum system describing the interaction of neutrons with an atom for the crystalline lattice, are retrieved.