A thermodynamic description of the glass transition: an exact one-dimensional example

An exact solution describing the properties of the fluid and the glass transition in terms of the underlying configurational landscape is obtained for a binary mixture of nonadditive hard rods on a line. The role of dynamics usually associated with the glass transition can be replaced by applying constraints to the fluid which trap the system in a single basin on the landscape. The glass transition can then be fully described in terms of thermodynamics. The entropy of the system decreases at the glass transition and the entropy of any glass relative to another is shown to be zero, which suggests that there is no residual entropy associated with the glasses.