Complexity as the driving force for dynamical glassy transitions

Abstract

Aspects of the dynamical glass transition are considered within a mean field spin glass model. At the dynamical transition the the system condenses in a state of lower entropy. The difference, the information entropy or complexity, is calculated by analysis of the metastable (TAP) states. It increases for lower temperatures, showing that more and more free energy barriers cannot be overcome on accessible times scales. Near $T_c$ the total glassy free energy lies below the paramagnetic one, which makes the transition unavoidable from a thermodynamic point of view. The multitude of glassy states implies an extensive difference between the average specific heat and the derivative of the average internal energy.