Linear representations of probabilistic transformations induced by context transitions

By using straightforward frequency arguments we classify transformations of probabilities which can be generated by transition from one preparation procedure (context) to another. There are three classes of transformations corresponding to statistical deviations of different magnitudes: (a) trigonometric; (b) hyperbolic; (c) hypertrigonometric. Each class is characterized by a perturbation of the ‘classical probabilistic rule’: (a) cos θ, (b) cosh θ, (c) both cos θ and cosh θ. Trigonometric transformations correspond to context-transitions that induce statistical deviations of relatively small magnitudes (in classical physics negligibly small); hyperbolic relatively large magnitudes. We found that not only preparation procedures described by conventional quantum formalism can have trigonometric probabilistic behaviour. We propose generalizations of C-linear space probabilistic calculus to describe non quantum (trigonometric and hyperbolic) probabilistic transformations.