We analytically investigate the population and coherence dynamics and relaxations in the vibrational energy transport in molecules. The corresponding two time scales t1 and t2 are explored. Coherence-population entanglement is found to considerably promote the time scale t2 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 t1 < t2. 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 D2O. Finally we explore the coherence effect on the heat current at the macroscopic level.
