  Two-level electron-phonon systems with reflection symmetry linearly coupled
to one or two phonon modes (exciton and E$\otimes(b_1+b_2)$ Jahn-Teller model)
exhibit strong enhancement of quantum fluctuations of the phonon coordinates
and momenta due to the complex interplay of quantum fluctuations and
nonlinearities inherent to the models. We show that for the complex correlated
quantum fluctuations of the anisotropic two-level systems the Shannon entropies
of phonon coordinate and momentum and their sum yield their proper global
description. On the other hand, the variance measures of the Heisenberg
uncertainties suffer from several shortcomings to provide proper description of
the fluctuations. Wave functions, related entropies and variances were
determined by direct numerical simulations. Illustrative variational
calculations were performed to demonstrate the effect on an analytically
tractable exciton model.
