Decoherence dynamics of quarkonia is studied in the high-temperature deconfined phase SU($N_c$) gauge theories. In particular, we analyze symmetry properties stochastic potential model and find a novel "event-by-event" for $N_c=2$ case, similar to $G$-parity hadronic systems. This constrains relation between diagonal off-diagonal components quarkonium density matrix, leaving latter be finite at...