No-signaling-in-time as a condition for macrorealism: the case of neutrino oscillations

We consider two necessary and sufficient conditions for macrorealism recently appeared in the literature, known as no-signaling-in-time and arrow-of-time conditions, respectively, and study them in the context of neutrino flavor transitions, within both the plane wave description and the wave packet approach. We then compare the outcome of the above investigation with the implication of various formulations of Leggett-Garg inequalities. In particular, we show that the fulfillment of the addressed conditions for macrorealism in neutrino oscillations implies the fulfillment of the Leggett-Garg inequalities, whereas the converse is not true. Finally, in the framework of wave packet approach, we also prove that, for distances longer than the coherence length, the no-signaling-in-time condition is always violated whilst the Leggett-Garg inequalities are not.