Asymptotic lower bound for the relative disparities of truncated-path-integral partition functions

Any truncated-path-integral partition function of a nonrelativistic quantum system in thermodynamic equilibrium one obtained by means of the Feynman p ath-interval-procedure using a finite number of such integrals - is known t o have a value not less than that of the exact one corresponding to it. A r igorous asymptotic lower bound obtained for the relative disparity in their values - the difference in their values divided by that of the exact parti tion function confirms asymptotic positive-definiteness of the original upp er bound. Values determined directly for a linear harmonic oscillator agree asymptotically with values of they bound.