TABLE OF CONTENTS Classical statistical mechanics is based on the assumption that all matters are composed of a myriad of small discrete particles, such as molecules and atoms, in any given macroscopic volume. [1] [5] There are about N = 2.5 10 16 molecules per cubic millimeter of air at standard conditions (25 C and 1 atm). These particles are in continuous random motion, which generally obeys the laws of classical mechanics. A complete microscopic description of a system requires the identification of the position r i ( t) and velocity v i ( t) of each particle (here, subscript i indicates the ith particle) at any time. For a simple system of N molecules in a box of volume V, one can write Newton's law of motion for each molecule as
where F ij is the intermolecular force that the jth molecule exerts on the ith molecule, and m i is the mass of the ith molecule. The initial position and velocity, as well as the nature of collisions among particles and that between particles and the walls of the box, must be specified in order to solve the N equations. Although this approach is straightforward, there are two major barriers. First, the intermolecular forces or potentials are often complicated and difficult to determine. Second, the solution of Eq. (3.1) requires significant computer resources even for rather simple problems. Statistical methods are often...
