Theoretical foundations of classical statistical mechanics

Abstract After a review of the basic definitions and laws of thermodynamics, Chapter 2 builds the foundations of classical statistical mechanics. First, the concepts classical microscopic states or “microstates” in phase space and classical ensembles as phase-space distributions are introduced. Following this, the connection between the time evolution prescribed by Hamilton’s equations of motion and the conservation laws of phase-space volume and phase-space probability are used to derive two fundamental results in classical statistical mechanics: Liouville’s theorem and the Liouville equation for the evolution of the ensemble distribution in time and phase space. Liouville’s equation is then solved under equilibrium conditions to yield the general form of a classical equilibrium ensemble