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We consider two necessary and sufficient conditions for macrorealism recentlyappeared in the literature, known as no-signaling-in-time and arrow-of-timeconditions, respectively, and study them in the context of neutrino flavortransitions, within both the plane wave description and the wave packetapproach. We then compare the outcome of the above investigation with theimplication of various formulations of Leggett--Garg inequalities. Inparticular, we show that the fulfillment of the addressed conditions formacrorealism in neutrino oscillations implies the fulfillment of Leggett--Garginequalities, whereas the converse is not true. Finally, in the framework ofwave packet approach, we also prove that, for distances longer than thecoherence length, the no-signaling-in-time condition is always violated whilstLeggett--Garg inequalities are not.

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