ABSTRACT
Thermodynamics acts as a law of large numbers in constraining the energy exchange in macroscopic systems. In previous chapters we have developed a scenario for its application to the glassy state and discussed its limits. A different fundamental question is which mechanism lies at the origin of the slow dynamics that leads to glassy behavior. Obviously, this has a strong system-dependent component, though certain types of universality are expected. A number of scenarios that are known in literature will be discussed in the present chapter. In particular, we will give a short presentation of the mode-coupling theory and of the mean-field replica theory applied to models related to structural glasses, both with and without ad hoc quenched disorder. We will, then, dedicate some more space to the state of the art for what concerns the avoided critical point theory and the random first order transition theory for the mosaic state. Some theories have been widely referred to in the previous chapters and we report them for self-consistency and to provide up-to-date bibliography for interested readers. Some other theories are, in our opinion, interesting recent developments, whose properties we critically analyze and discuss, trying, as well, to compare different points of view in the literature. Many other approaches, among which we mention those of Schulz [1998] and Franz [2005, 2006], fall outside the scope of this book.
