TABLE OF CONTENTS Statistical mechanics involves determination of the most probable state and equilibrium distributions, as well as evaluation of the thermodynamic properties in the equilibrium states. Kinetic theory deals with the local average of particle properties and can be applied to nonequilibrium conditions to derive transport equations. [1] [7] Kinetic theory, statistical mechanics, and molecular dynamics are based on the same hypotheses; they are closely related and overlap each other in some aspects. Knowledge of kinetic theory is important to understanding gas dynamics, as well as electronic and thermal transport phenomena in solid materials.
In this chapter, we first introduce the simple kinetic theory of ideal gases based on the mean-free-path approximation. While it can help us obtain the microscopic formulation of several familiar transport equations and properties, the simple kinetic theory is limited to local equilibrium and, hence, is good only for time durations much longer than the mechanistic timescale, called the relaxation time. The advanced kinetic theory is based on the Boltzmann transport equation (BTE), which will also be presented in this chapter. The BTE is an integro-differential equation of the distribution function in terms of space, velocity, and time. It takes into account changes in the distribution function caused by external forces and collisions between particles. Many macroscopic phenomenological equations, such as Fourier's law of heat conduction, the Navier-Stokes equation for viscous flow, and the equation of radiative transfer for photons and phonons, can be derived from the BTE, under the assumption of local equilibrium. Finally,...
