Nonadditive Geometric Phase and Correlated CP Effects in Entangled Neutral Meson Systems

We investigate the geometric structure associated with CP-violating dynamics in entangled neutral meson systems. We formulate the time-dependent geometric phase for the correlated two-meson state and analyze its system-dependent behavior across different neutral meson mixing scenarios. We demonstrate that the geometric phase associated with the entangled state cannot, in general, be expressed as a sum of independent single-meson contributions, indicating the presence of genuinely entanglement-induced geometric effects. Furthermore, we show how CP violation enters the geometric phase through mixing, leading to a rephasing-invariant geometric structure of correlated evolution that remains indirectly sensitive to the mixing parameters. These results clarify the geometric characterization of entanglement and CP violation in neutral meson systems.