Potential energy landscape description of supercooled liquids and glasses

These notes review the potential energy landscape thermodynamic formalism and some of its recent applications to the study of supercooled glass forming liquids. They also review the techniques which have been recently developed to quantify the statistical properties of the landscape, i.e. the number and the distribution in energy of the local minima of the surface for bulk systems. A critical examination of the approximations involved in such a calculation and results for models of simple and molecular liquids are reported. Finally, these notes discuss how an equation of state, expressed only in terms of statistical properties of the landscape, can be derived and under which conditions such an equation of state can be generalized to describe out-of-equilibrium liquids.