Invariants of motion are constructed departing from the Gibbs entropy. The method we applied also allows us to find the subspace of a real vector space to which the system is confined to during its temporal evolution. We also find that the Uncertainty Principle is itself an invariant of motion...

We demonstrate that when the Gibbs entropy is an invariant of motion, following Information Theory procedures it is possible to define a generalized metric phase space for the temporal evolution of the mean values of a given Hamiltonian. The metric is positive definite and this fact leads to a...

Using the generalized Ehrenfest theorem the dynamics of the mean values of a complete set of non-commuting observables (CSNCO) associated to a given Hamiltonian is expressed. We found refined time-dependent invariants of motion (TDIM) for the CSNCO, and associated them with different Lie...