ABSTRACT
In the nineteenth century, Boltzmann explored the connection between entropy and statistical probability. In the development of the statistical approach, the authors use a microscopic description on the basis of quantum mechanics and enumerate the states of systems of interest, specifically for the ideal gas and ideal spin systems. A classical phase space description of fluids, which is complementary to the quantum mechanical description, is also discussed. In statistical calculations, it is necessary to specify the various states that are available for the particular system considered. In the high-temperature and low-particle-density limit, the particle statistics become unimportant. The labeled quantum states for the two model systems permit the reader to count states in a particular energy range.
