With the miniaturization of devices, size and interface effects become increasingly important for the properties and performances of nanomaterials. Here, we present a thermodynamic approach to the mechanism behind size-induced unusual behavior in the phase stabilities of ferromagnetic (FM), antiferromagnetic (AFM), ferroelectric (FE), and superconductive (SC) nanocrystals, which are different dramatically from their bulk counterparts. This method is based on the Lindemann criterion for melting, Mott s expression for the vibrational melting entropy, and the Shi model for the size-dependent melting temperature. Simple and unified functions, without any adjustable parameter, are established for the size and interface dependences of thermal and phase stabilities of FM, AFM, FE and SC nanocrystals. According to these analytic functions, as the size of nanocrystals is reduced, the thermal and phase stabilities may strengthen or weaken, depending on the confluence of the surface/volume ratio of nanocrystals and the FM(AFM, FE or SC)/substrate interface situations. The validity of this model is confirmed by a large number of experimental results. This theory will be significant for the choice of materials and the design of devices for practical application.