Boltzmann Statistics

When a system is held at a fixed temperature, its higher-energy states are less probable than its lower energy states by an amount that depends on how the energy compares to the temperature. The formula that quantifies this idea is called the Boltzmann distribution. This chapter derives the Boltzmann distribution and shows how to use it to predict the thermal behavior of any system whose microscopic states we can enumerate. The examples go beyond the three simple model systems studied already in Chapters 2 and 3 to include detailed properties of gases, stellar spectra, and paramagnetic materials.