Stochastic particle models in non-equilibrium physics

Over the last twenty years or so, numerous microscopic models have been proposed to study the transport of heat or particles through extended systems. The aim of the 2016-2017 lecture was to take stock of several recent advances and of questions that have remained open. For some systems, such as lattice gas models, a macroscopic theory has been available since the early 2000s, the " theory of macroscopic fluctuations ", which can be seen as a generalization of a Langevin dynamics to extended systems. This theory makes it possible to understand the existence of long-range correlations, to calculate the functions of large current and density deviations, and to predict phase transitions. Where comparison is possible, as in the case of exclusion models, it is consistent with calculations based on microscopic descriptions. More natural transport models, such as mechanical systems that conserve both energy and momentum, are more difficult to tackle, despite some major recent advances.