Nonextensive quantum statistics and saturation of the PMD-SQS optimality   limit in hadron-hadron scattering
  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. 
D. B. Ion (1), M. L. Ion (2) ((1) IFIN-HH, Bucharest, Romania, (2)   University of Bucharest, Romania)