  Macrorealism formalizes the intuitive notion that at any given time the
system occupies a definite state and that the evolution of the system is
independent of the measurements performed on it, in contrast to the principles
of quantum mechanics. In this study, we carry out a comparative analysis
between three-time Leggett--Garg-type inequalities and the conditions of
no-signaling-in-time and arrow-of-time for macrorealism within the context of
meson oscillations. Our findings indicate that, under given initial conditions,
no violations of Leggett--Garg inequalities are observed. However,
no-signaling-in-time conditions are found to be violated, thereby revealing the
impossibility of applying a macrorealistic description to the analysis of meson
physics.
