DISAPPEARANCE OF TIME INTEGRALS OF EXACT MEMORY FUNCTIONS IN TIME-CONVOLUTION GENERALIZED MASTER-EQUATIONS

Memory functions in time-convolution Generalized Master Equations (GME ) for probabilities of finding a general system (interacting by a gene ral coupling with a true thermodynamic bath) in individual states an c onsidered without resorting to any approximation. After taking the the rmodynamic bath limit. time integrals from zero to infinite times of t he memories are considered. It is argued that these integrals entering , e.g., the usual naive Markov approximation converting GME the Pauli master (PME) equations are exactly zero. This implies long-time tails of memories (unobtainable by perturbational expansions) and slower-tha n-exponential long-time asymptotics of relaxation.