This chapter considers what would happen to a mixture with the statistical operator 𝗨 if a quantity 𝖱 with operator 𝖱 is measured in it. It then investigates the thermodynamics of quantum mechanical ensembles from two different points of view. First, the chapter assumes the validity of both of the fundamental laws of thermodynamics, and proceeds on this basis to calculation of the entropy of ensembles. In this effort the normal methods of phenomenological thermodynamics are applied, and quantum mechanics plays a role only insofar as these thermodynamic observations relate to objects whose behavior is regulated by the laws of quantum. Afterwards this chapter proves the validity of these fundamental laws in quantum mechanics. Next, the chapter introduces some reversibility and equilibrium problems. Finally, this chapter discusses the macroscopic measurement.
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