Comments on a model influence functional for quantum systems

We continue the study of a model non-Gaussian influence functional proposed by Allinger, Carmeli, and Chandler [J. Chem. Phys. 84, 1724 (1986)] to approximate the exact influence functional resulting from integrating out all quantum states but those of primary interest. The premise of this work is that the influence of many secondary states on a single primary state can be closely approximated by the influence of a degenerate level of states with equal coupling to the primary state. The degeneracy reflects the fluctuations possible among the secondary states and in fact can be associated with the partition function of the exact secondary states. The new calculations presented herein emphasize the importance of entropic-like effects properly described by this degeneracy, and for the models we examine, our basic premise is shown to be correct.