C.M. Sarris، نويسنده , , A.N. Proto، نويسنده ,
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 metric tensor, K(t), whose properties are well defined. Working with these properties we shown that: (a) the Generalized Uncertainty Principle (GUP), is always the summation over the principal minors of order 2 belonging to K(t); (b) several invariants of motion can be derived from the metric tensor; and (c) particularly, under certain conditions, the GUP itself, is also a motion invariant.