  In this paper, new results on the analysis in hadron-hadron scattering are
obtained by using the nonextensive quantum entropy and principle of minimum
distance in the space of quantum states (PMD-SQS). Using Tsallis-like
scattering entropies, the optimality as well as the nonextensive statistical
behavior of the quantum scattering systems are investigated in an unified
manner. A connection between optimal states obtained from the principle of
minimum distance in the space of quantum states and the most stringent (MaxEnt)
entropic bounds on Tsallis-like entropies for quantum scattering, is
established. The generalized entropic uncertainty relations as well as the
correlation between the nonextensivities p and q of the scattering statistics
are proved. New results on the experimental tests of the saturation of the
optimality limit}, as well as on the test of optimal entropic bands obtained by
using the experimental pion-nucleon, kaon-nucleon, antikaon-nucleon phase
shifts, are presented. The nonextensivity indices p and q are determined from
the experimental entropies by a fit with the optimal entropies obtained from
the principle of minimum distance in the space of states. Strong experimental
evidences for the p-nonextensivity index in the range p=0.6 with q=p/(2p-1)=3,
is obtained from the experimental data.
