  The Leggett-Garg inequality (LGI) as a temporal analogue of Bell's
inequality, derived using the notion of realism, is applied in a hitherto
unexplored context involving the weak interaction induced two-state
oscillations of decaying neutral kaons and neutrinos. The maximum violation of
LGI obtained from the quantum mechanical results is significantly higher for
the oscillating neutrinos compared to that for the kaons. Interestingly, the
effect of CP non-invariance for the kaon oscillation is to enhance this
violation while, for neutrinos, it is sensitive to the value of the mixing
parameter.
