Thermodynamics and statistic physics developed as one of the most fruitful physical concepts. The progressive nano-technology makes it necessary, the applicability for that already admitted concepts from classical thermodynamics on the microscopic level to examine. Questions about the extensivity of the energy and entropy, as well as about the existence of a temperature are just as important as the investigation of thermodynamic cyclic processes for quantum systems. This theses studies small quantum systems in nonequillibrium and may shed light on some new aspects of quantum thermodynamics. Heat conduction in driven as well as in undriven cases are examined on the basis of a possible local description.