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Abstract

In the generalized thermodynamics first discussed by FICK, partial energies may depend on several temperatures. The partial heats form a coupled system of PFAFFIans. In contrast to conventional thermodynamics an integrating factor does not exist for each of these PFAFFians, only a linear combination of them is an exact form. It is discussed, if the existence of absolute temperatures and entropy may be deduced from the integrability of systems in thermal contact. As the PFAFFians may be complete or incomplete integrable the proof is not a straightforward generalization of CARATHÉODORYS way.