Optimality, entropy and complexity for nonextensive quantum scattering

In this paper, by introducing [SJ(p),Sθ(q)] Tsallis-like entropies, the optimality and complexities as well as the nonextensive statistical behavior of the [J and θ]-quantum states in hadronic scatterings are investigated in an unified manner. A connection between optimal states obtained from the principle of minimum distance in the space of quantum states (PMD-SQS) and the most stringent (MaxEnt) entropic bounds on Tsallis-like entropies for quantum scattering is established. A measure of the complexity of quantum scattering in terms of Tsallis-like entropies is proposed. The generalized entropic uncertainty relations as well as a possible correlation between the nonextensivities p and q of the [J and θ]-statistics are proved. The results on the experimental tests of the PMD-SQS-optimality, as well as on the optimal entropic bands and optimal complexity, obtained by using the experimental pion–nucleon pion–nucleus phase shifts, are presented. The nonextensivity indices p and q are determined from the experimental entropies by a fit with the optimal entropies [SJo1(p),Sθo1(q)] obtained from the principle of minimum distance in the space of states. In this way strong experimental evidences for the p-nonextensivities in the range 0.5 p 0.6 with q=p/(2p−1)>3 are obtained [with high accuracy (CL>99%)] from the experimental data of pion–nucleon and pion–nucleus scatterings.