Why does volume sometimes decrease with the increase of temperature

Both common wisdom and physical science indicate that volume increases with temperature though it has been observed frequently in both natural and man-made materials that volume sometimes decreases with the increase of temperature. The answer to the question 'Why does volume sometimes decrease with the increase of temperature?' has remained elusive for centuries. In last decade, we have developed a multiscale entropy approach, introduced as zentropy approach in the present work, to understand and predict the change of volume as a function of temperature. It is shown that a phase at high temperatures is composed of both the ground-state configuration and multiple nonground-state configurations. It is demonstrated that when the volumes of nonground-state configurations are smaller than that of the ground-state configuration, the volume of the phase may decrease with the increase of temperature in certain range of temperature-pressure combinations. As examples, positive and negative divergencies of volume with respect to temperature are predicted at the critical points of Ce and Fe3Pt, respectively, along with the temperature and pressure ranges for abnormally positive and negative changes of their volumes with respect to temperature. The authors believe that the zentropy approach is applicable to predict anomalies of other physical properties of phases.