Additivity and Extensivity of the Clausius Entropy and Other Thermodynamic Quantities

It is shown that the Clausius entropy and the internal energy can be taken to be additive for systems existing next to each other, contemporaneously, and without relative speed. Also, it is shown that any thermodynamic state quantity is extensive if it is additive and if its volume density is finite. It is argued that for many state quantities the assumption of extensivity can be replaced by the assumption of finite density. The point of view is the macroscopic and non-statistical one of classical thermodynamics.