The limit of small entropy production is reached in relaxing systems long after preparation, and in stationary driven systems in the limit of small driving power. Surprisingly, for extended systems this limit is not in general the Gibbs-Boltzmann distribution, or a small departure from it....

In this note I introduce some techniques to treat systems in contact with (stochastic) thermal baths. The methods and the level of rigour are those of theoretical physics.

We discuss the general link between mode-coupling like equations (which serve as the basis of some recent theories of supercooled liquids) and the dynamical equations governing mean-field spin-glass models, or the dynamics of a particle in a random potential. The physical consequences of this...