  We {\it analytically} investigate the population and coherence dynamics and
relaxations in the vibrational energy transport in molecules. The corresponding
two time scales $t_1$ and $t_2$ are explored. Coherence-population entanglement
is found to considerably promote the time scale $t_2$ for dephasing and the
amplitude of coherence. This is attributed to the suppression of the
environment-induced drift force by coherence. Moreover the population imbalance
(magnetization) is shown to be significantly amplified with the
coherence-population entanglement. Contrary to the previous studies, we exactly
elucidate a coherent process by showing $t_1<t_2$. We predict the relaxation of
vibrational and orientational dynamics of OH-stretching modes in agreement with
the recent experiments, when applied to the water molecules dissolved in
D$_2$O. Finally we explore the coherence effect on the heat current at the
macroscopic level.
