Nonlinear extension of the quantum dynamical semigroup

In this paper we consider deterministic nonlinear time evolutions satisfying so called convex quasi-linearity condition. Such preserve the equivalence of ensembles and therefore are free from problems with signaling. We show that if family linear non-trace-preserving maps satisfies semigroup property then generated quasi-linear operations also possesses property. Next generalize Gorini-Kossakowski-Sudarshan-Lindblad type equation for considered evolution. As examples discuss general qubit evolution in our model as well an extension Jaynes-Cummings model. apply formalism to spin density matrix a charged particle moving electromagnetic field flavor solar neutrinos.