Nonlinear quantum evolution does not imply supraluminal communication

We build up simple models of quantum evolution showing that nonlinearity does not necessarily imply either the possibility of faster-than-light communications or the violation of the second law of thermodynamics. We offer counterexamples proving that conditions of no supraluminal communication considered in the literature as necessary and sufficient are actually only necessary. We formulate conditions and show that this preclusion only entails the linearity of reduced dynamics, thus reopening the possibility to unexplored nonlinear joint evolutions. We make constant use of the Bloch representation of finite-dimensional quantum systems to express our results