correlation length which produces diverging relaxation times as well as diverging static susceptiblities [@Kirkpatrick89; @Sethna91; @Kivelson95; @Ernst91; @Dasgupta91; @Menon95]. More recently Mezard and Parisi [@Mezard99; @Parisi97b] have argued that the underlying transition is actually a random first order transition signaled by a jump discontinuity in the specific heat.

Experimentally the glass transition is characterized by both kinetic and thermodynamic features. For example in the supercooled liquid kinetic quantities such as the viscosity and relaxation time grow rapidly as the temperature is lowered. When the system falls out of equilibrium below a certain temperature, thermodynamic quantities exhibit features reflecting the glass transition. For example as the system is cooled the specific heat has a step–like form and the dielectric constant exhibits a peak at a frequency dependent temperature.

In an effort to better characterize the glass transition we introduce a novel probe which we call a generalized compressibility [@Yvon58]. Unlike the specific heat which monitors energy fluctuations, this linear compressibility is a function of the microscopic structure of the system: it depends solely on the positions of the particles and not on their previous history. Since we do not need to compare the system’s state at different times, it is not 