Introduction

Statistical mechanics is a very fruitful and successful combination of (i) the basic laws of microscopic dynamics for a system of particles with (ii) the laws of large numbers. This branch of theoretical physics attempts to describe the macroscopic properties of a large system of particles, such as one would find in a fluid or solid, in terms of the average properties of a large ensemble of mechanically identical systems which satisfy the same macroscopic constraints as the particular system of interest. The macroscopic phenomena that concern us in this book are those which fall under the general heading of irreversible thermodynamics, in general, or of fluid dynamics in particular. We shall be concerned with the second law of thermodynamics, more specifically, with the increase of entropy in irreversible processes. The fundamental problem is to reconcile the apparent irreversible behavior of macroscopic systems with the reversible, microscopic laws of mechanics which underly this macroscopic behavior. This problem hats actively engaged physicists and mathematicians for well over a century.

The law of large numbers and the laws of mechanics

Many features of the solution to this problem were clear already to the founders of the subject, Maxwell, Boltzmann, and Gibbs, among others. The notion that equilibrium thermodynamics and fluid dynamics have a molecular basis is one of the central scientific advances of the 19th century. Of particular interest to us here is the work of Maxwell and Boltzmann, who tried to understand the laws of entropy increase in spontaneous natural processes on the basis of the classical dynamics of many-particle systems.