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Besides the growing interest in old concepts like temperature and entropy atthe nanoscale, theories of relaxation and transport have recently regained alot of attention. With the electronic circuits and computer chips gettingsmaller and smaller, a fresh look should be appropriate on the equilibrium andnonequilibrium thermodynamics at small length scales far below thethermodynamic limit, i.e. on the theoretical understanding of originalmacroscopic processes, e.g. transport of energy, heat, charge, mass,magnetization etc. Only from the foundations of a theory its limits ofapplicability may be inferred. This review tries to give an overview of thebackground and recent developments in the field of nonequilibrium quantumthermodynamics focusing on the transport of heat in small quantum systems.Comment: 30 pages, 10 figures, review articl

MICROSCOPIC QUANTUM MECHANICAL FOUNDATION OF FOURIER'S LAW