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