Abstract
Any truncated-path-integral partition function of a nonrelativistic quantum system in thermodynamic equilibrium—one obtained by means of the Feynman path-integral-procedure using a finite number of such integrals—is known to have a value not less than that of the exact one corresponding to it. A rigorous asymptotic lower bound obtained for the relative disparity in their values—the difference in their values divided by that of the exact partition function— confirms asymptotic positive-definiteness of the original upper bound. Values determined directly for a linear harmonic oscillator agree asymptotically with values of they bound.
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Golden, S. Asymptotic Lower Bound for the Relative Disparities of Truncated-Path-Integral Partition Functions. Journal of Statistical Physics 95, 495–502 (1999). https://doi.org/10.1023/A:1004550100048
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DOI: https://doi.org/10.1023/A:1004550100048