PHENOMENOLOGICAL DETERMINISMS IN AN HAMILTONIAN COSMOS

We show that the classical equations that govern exactly in both time directions the fundamental information, and express at each time the state of a Boltzmann-Gibbs hamiltonian cosmos, entails the existence of a specific phenomenological fraction of the fundamental information. Observers may anticipate accurately this fundamental information, but exclusively along a preferential time direction, identified with the arrow of time. That phenomenological fraction is thus submitted to a phenomenological determinism applicable only along the arrow of time. It permanently generates non-phenomenological components of the fundamental information. The latter accumulates undamped, but experiences an exponentially fast complexification. This complexification makes the accumulated non-phenomenological information definitively inaccessible to the observers, but at the same time unable to influence the evolution of the phenomenological information. That evolution is thus autonomous and submitted to a phenomenological determinism.