Nonequilibrium statistical mechanics of a solid immersed in a continuum

In the introductory part of this survey, we briefly discuss the problems of nonequilibrium statistical physics that arise in the study of energy transport in solids as well as the results available at the moment. In the main part of the survey, we explain, compare, and generalize results obtained in our previous works. We study the dynamics and energy transport in Hamiltonian systems of particles where each particle is weakly perturbed by the interaction with its own stochastic Langevin thermostat. Such systems can be regarded as models of solids that interact weakly with a continuum.