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In our previous paper (I) we derived information geometric objects from thetwo parameter generalized entropy of Hanel and Thurner (2011), using the c,dparameters as labels of the corresponding manifolds. Here we follow acompletely different approach by considering these parameters as coordinates ofour information manifolds. This gives a manageable two-dimensional manifoldamenable to easy manipulations but most importantly it offers a directcharacterization of complex systems in terms of the pair of the c,d values. Asa result we obtain certain characteristic values from the scalar curvaturewhich we could conjecture that they represent complex systems with specificbehavior. It is further observed that the boundary values of the c,d parameterswhich characterize the Hanel-Thurner classification are in some sense singular.This asks for a regularization scheme which we try to establish.

Towards an Information Geometric characterization/classification of Complex Systems. II. Critical Parameter values from the (c,d)-manifold