Tsallis' deformation parameter q quantifies the classical-quantum   transition
  We investigate the classical limit of a type of semiclassical evolution, the pertinent system representing the interaction between matter and a given field. On using as a quantifier of the ensuing dynamics Tsallis q-entropy, we encounter that it not only appropriately describes the quantum-classical transition, but that the associated deformation-parameter q itself characterizes the different regimes involved in the process, detecting the most salient fine details of the changeover. 
A.M. Kowalski, M.T. Martin, A. Plastino, L. Zunino