Illustration: Alan Stonebraker

Figure 1: The graph shows the specific heat as a function of $T$ for bulk ice (blue) and small ice clusters (red). The specific heat shows the ratio of the system’s internal energy change to changes in the system’s temperature. In other words, it represents the amount of energy we need to supply to the system to increase its temperature by an infinitesimal amount. This ratio depends on the temperature. As $T$ increases, more vibrational quanta are available to be excited and therefore, for a small increase in temperature, more energy can be stored in the system than at lower $T$. The melting of ice is a first-order phase transition. There is a discontinuous change in the entropy, associated to the onset of the large configurational entropy of the liquid. This discontinuity is related to a peak that appears in the specific heat curve of the bulk system (blue) as a function of the temperature—this is called the latent heat peak. The melting transition observed for the small water clusters (red) studied by Hock et al. happens at a lower temperature. This temperature depends on the size of the cluster (the smaller the size, the lower the melting transition temperature). It also differs from a normal first-order phase transition because the latent heat peak is not observed.