Ergodicity in glass relaxation

We derive an equation for the glass relaxation. In the derivation, the Zwanzig-Mori projection method is not applied explicitly, which makes our equation different from the mode coupling theory. Due to the nonlinearity, it is difficult to solve the equation to get the full behaviors of the glass relaxation. But we can simplify the equation when time approaches infinity and obtain the static result analytically. The static result shows that the density correlation function decays to zero finally, meaning that the glass relaxation is ergodic. In this study, we also find that the force fluctuation of one individual particle averaged in the glass is sensitive to the temperature and is suggested to be a parameter to reflect the structural transition for the glass relaxation.