本論文主要包含兩部分的研究工作，第一部份的研究工作，主要進行相平衡 (phase equilibrium )現象的計算與分析，第二部分的工作，則針對液態--玻璃相變（liquid-glass transition）的現象進行研究。我們所研究的對象雖然都是帶電膠體系統（charged colloidal dispersion），但是從統計力學的角度來看，第一部份的工作與第二部分的工作兩者極為不同，這兩部分各別涉及了「平衡統計」與「非平衡統計」兩個領域。 This thesis embodies two parts. The …rst part concerns with calculations of phase equilibrium phenomena and the methodology and analysis we proposed for a thorough un- derstanding of phase transition. The second part aims at liquid-glass transition phenomena applying the microscopic mode coupling theory to study the dynamical behaviors and ex- ploiting the factors leading to glass transition. Although the physical system of interest in both parts is the charge-colloidal dispersion, the physical process is, however, fundamentally di¤erent from the viewpoint of statistical mechanics. The …rst part describes equilibrium scenario. In this part, we revisited the present status of thermodynamic theories applied to phase-diagram calculations. We put forth in this thesis a novel means of phase-diagram calculations and introduce free energy landscape analysis to gain insight into phase separa- tion phenomena. The second part, on the other hand, deals with nonequilibrium processes. Here we investigate how the colloidal particles embedded in disperse medium can be driven to a glassy or non-ergodic state. The mechanism of glass transition and how the mode coupling theory was used to predict and analyze its occurrence are tersely covered in the present work. We describe below the essential problems that we have touched on in these two parts.