Statistical entropy From micro to macro
This chapter introduces the microscopic interpretation of entropy, what quantifies the "missing" degrees of freedom not accounted for in macroscopic descriptions. It explains the foundation for statistical mechanics. Tutorial introductions to probability theory are often given in books on statistical mechanics. The chapter also introduces some basic combinatorial ideas. It considers two ways of coarse graining the description of a classical gas of N atoms so that its microstates are specified in such a way as to be countable. The phase-space density function is a fundamental object of study in non-equilibrium statistical mechanics. The chapter outlines the Sackur-Tetrode analysis, because a fundamental discovery was made in the process. The Sackur-Tetrode formula provides experimental confirmation (from thermodynamic measurements) of the picture that emerges from quantum mechanics that each particle carries with it a fundamental volume of phase space.