Statistical Mechanics Derived From Quantum Mechanics

A pedagogical derivation of statistical mechanics from quantum mechanics is provided, by means of open quantum systems. Besides, a new definition of Boltzmann entropy for a quantum closed system is also given to count microstates in a way consistent with the superposition principle. In particular, this new Boltzmann entropy is a constant that depends only on the dimension of the system's relevant Hilbert subspace. Finally, thermodynamics for quantum systems is investigated formally.