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Energy flow and thermo-electricity in atomic and molecular junctions

Advances in the fabrication and characterization of nanoscale systems now allow for a deeper understanding of one of the most basic issues in science and technology: the flow of energy at the microscopic level. In this Colloquium we survey recent advances and present understanding of physical mechanisms of energy transport in nanostructures, focusing mainly on molecular junctions and atomic wires. We examine basic issues such as thermal conductivity, thermoelectricity, local temperature and heating, and the relation between energy current density and temperature gradient - known as Fourier's law. We critically report on both theoretical and experimental progress in each of these issues, and discuss future research opportunities in the field.