  On a family of classical dynamical systems on the 2-torus, we perform a
discretization procedure similar to the Anti-Wick quantization. Such a
discretization is performed by using a particular class of states, fulfilling
an appropriate dynamical localization property, typical of quantum Coherent
States. The same set of states is involved in the construction of a quantum
entropy, that we test on the discrete approximants; a correspondence with the
classical metric entropy of Kolmogorov-Sinai is found only over time scales
that are logarithmic in the discretization parameter.
