FROM CONVOLUTIONLESS GENERALIZED MASTER TO FINITE-COUPLING PAULI MASTER-EQUATIONS

Time-convolutionless Generalized Master Equations (TCL-GME) for probab ilities of finding a system in a general state, irrespective of the st ate of the thermodynamic bath, are investigated. For general systems i nteracting with a genuine bath with a continuous spectrum described by time-independent system + bath Hamiltonians and after the thermodynam ic limit for the bath, the long-time asymptotics of time-dependent coe fficients can be taken as counterparts of Pauli-Master-Equation (PME) transfer rates. Here, within TCL-GME, asymptotics of these coefficient s is calculated without resorting to any approximation. In the lowest order, these coefficients are known to turn to the usual Fermi Golden Rule transfer rates. Anyway, we argue that if the exact form of these coefficients has a long-time limit, this limit is inevitably equal to zero. This makes the possibility to derive standard markovian finite-c oupling Pauli, rate or balance equations as long-time asymptotics to T CL-GME illusory.