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Heat Flow in Classical and Quantum Systems and Thermal Rectification

The understanding of the underlying dynamical mechanisms which determine the macroscopic laws of heat conduction is a long standing task of non-equilibrium statistical mechanics. A better understanding of the mechanism of heat conduction may lead to potentially interesting applications based on the possibility to control the heat flow. Indeed, different models of thermal rectifiers has been recently proposed in which heat can flow preferentially in one direction. Although these models are far away from a prototype realization, the underlying mechanisms are of very general nature and, as such, are suitable of improvement and may eventually lead to real applications. We briefly discuss the problem of heat transport in classical and quantum systems and its relation to the chaoticity of the dynamics. We then study the phenomenon of thermal rectification and briefly discuss the different types of microscopic mechanisms that lead to the rectification of heat flow.