  We study the entropy time evolution of a quantum mechanical model, which is
frequently used as a prototype for Anderson's localization. Recently Latora and
Baranger [V. Latora, M. Baranger, Phys. Rev.Lett. 82, 520(1999)] found that
there exist three entropy regimes, a transient regime of passage from dynamics
to thermodynamics, a linear in time regime of entropy increase, namely a
thermodynamic regime of Kolmogorov kind, and a saturation regime. We use the
non-extensive entropic indicator recently advocated by Tsallis [ C. Tsallis, J.
Stat. Phys. 52, 479 (1988)] with a mobile entropic index q, and we find that
with the adoption of the ``magic'' value q = Q = 1/2 the Kolmogorov regime
becomes more extended and more distinct than with the traditional entropic
index q = 1. We adopt a two-site model to explain these properties by means of
an analytical treatment and we argue that Q =1/2 might be a typical signature
of the occurrence of Anderson's localization.
