In the framework of deterministic finslerian models, a mechanism producing
dissipative dynamics at the Planck scale is introduced. It is based on a
geometric evolution from Finsler to Riemann structures defined in ${\bf TM}$.
Quantum states are generated and interpreted as equivalence classes, composed
by the configurations that evolve through an internal dynamics, to the same
final state. The existence of an hermitian scalar product in an associated
linear space is discussed and related with the quantum pre-Hilbert space. This
hermitian product emerges from geometric and statistical considerations. Our
scheme recovers the main ingredients of the usual Quantum Mechanics. Several
testable consequences of our scheme are discussed and compared with usual
Quantum Mechanics. A tentative solution of the cosmological constant problem is
proposed, as well as a mechanism for the absence of quantum interferences at
classical scales.