“…The coupling with the environment has a non-negligible influence on the dynamics of many-particle systems in both classical and quantum regimes. Due to a vast number of applications such as, cold atoms, [2,3,4,5], electronic devices [6], quantum circuits, [7,8] condensed matter, [6,9], quantum optics [10,11], traffic models [12], the theory of open quantum system has become a topic of great interest in recent years. Within the Markovian approximation, an open system (reduced) density matrix evolves via the Lindblad master equation, [13,14,15,16,17]…”