In this chapter, the analytical embedded atom method and calculating Gibbs free energy method are introduced briefly. Combining these methods with molecular dynamic and Monte Carlo techniques, thermodynamics of nano-silver and alloy particles have been studied systematically. For silver nanoparticles, calculations for melting temperature, molar heat of fusion, molar entropy of fusion, and temperature dependences of entropy and specific heat capacity indicate that these thermodynamic properties can be divided into two parts: bulk quantity and surface quantity, and surface atoms are dominant for the size effect on the thermodynamic properties of nanoparticles. Isothermal grain growth behaviors of nanocrystalline Ag shows that the small grain size and high temperature accelerate the grain growth. The grain growth processes of nanocrystalline Ag are well characterized by a power-law growth curve, followed by a linear relaxation stage. Beside grain boundary migration and grain rotation mechanisms, the dislocations serve as the intermediate role in the grain growth process. The isothermal melting in nanocrystalline Ag and crystallization from supercooled liquid indicate that melting at a fixed temperature in nanocrystalline materials is a continuous process, which originates from the grain boundary network. The crystallization from supercooled liquid is characterized by three characteristic stages: nucleation, rapid growth of nucleus, and slow structural relaxation. The homogeneous nucleation occurs at a larger supercooling temperature, which has an important effect on the process of crystallization and the subsequent crystalline texture. The kinetics of transition from liquid to solid is well described by the Johnson-Mehl-Avrami equation. By extrapolating the mean grain size of nanocrystal to an infinitesimal value, we have obtained amorphous model from Voronoi construction. From nanocrystal to amorphous state, the curve of melting temperature exhibits three characteristic regions. As mean grain size above about 3.8 nm for Ag, the melting temperatures decrease linearly with the reciprocal of grain size. With further decreasing grain size, the melting temperatures almost keep a constant. This is because the dominant factor on melting temperature of nanocrystal shifts from grain phase to grain boundary one. As a result of fundamental difference in structure, the amorphous has a much lower solid-to-liquid transformation temperature than that of nanocrystal.