## Statistical Mechanics

Donald A. McQuarrie University of California, Davis

With this edition, University Science Books becomes the publisher of both my *Statistical Thermodynamics* and *Statistical Mechanics* books. I would like to

thank the publisher, Bruce Armbruster, for his continual commitment to

quality textbook publishing in the sciences.

*Statistical Mechanics* is the extended version of my earlier text, *Statistical Thermodynamics*. The present volume is intended primarily for a

two-semester course or for a second one-semester course in statistical

mechanics. Whereas *Statistical Thermodynamics* deals principally with

equilibrium systems whose particles are either independent or effectively

independent, *Statistical Mechanics* treats equilibrium systems whose

particles are strongly interacting as well as nonequilibrium systems. The

first twelve chapters of this book also form the first chapters in *Statistical Thermodynamics*, while the next ten chapters, 13-22, appear only

in *Statistical Mechanics*. Chapter 13 deals with the radial distribution

function approach to liquids, and Chapter 14 is a fairly detailed discussion

of statistical mechanical perturbation theories of liquids. These theories

were developed in the late 1960s and early 1970s and have brought the

numerical calculation of the thermodynamic properties of simple dense fluids

to a practical level. A number of the problems at the end of the Chapter 14

require the student to calculate such properties and compare the results to

experimental data. Chapter 15, on ionic solutions, is the last chapter on

equilibrium systems. Section 15-2 is an introduction to

advances in ionic solution theory that were developed in the 1970s

and that now allow one to calculate the thermodynamic properties of simple ionic

solutions up to concentrations of 2 molar.

Chapters 16-22 treat systems that are not in equilibrium. Chapters 16 and

17 are meant to be somewhat of a review, although admittedly much of the

material, particularly in Chapter 17, will be new. Nevertheless, these two

chapters do serve as a background for the rest. Chapter 18 presents the

rigorous kinetic theory of gases as formulated through the Boltzmann

equation, the famous integro-differential equation whose solution gives the

nonequilibrium distribution of a molecule in velocity space. The long-time

or equilibrium solution of the Boltzmann equation is the well-known

Maxwell-Boltzmann distribution (Chapter 7). Being an integro-differential

equation, it is not surprising that its solution is fairly involved. We

only outline the standard method of solution, called the Chapman-Enskog

method, in Section 19-1, and the next two sections are a practical

calculation of the transport properties of gases. In the last section of

Chapter 19 we discuss Enskog’s ad hoc extension of the Boltzmann equation to

dense hard-sphere fluids. Chapter 20, which presents the Langevin equation

and the Fokker-Planck equation, again is somewhat of a digression but does

serve as a background to Chapters 21 and 22.

The 1950s saw the beginning of the development of a new approach to

transport processes that has grown into one of the most active and fruitful

areas of nonequilibrium statistical mechanics. This work was initiated by

Green and Kubo, who showed that the phenomenological coefficients describing

many transport processes and time-dependent phenomena in general could be

written as integrals over a certain type of function called a

time-correlation function. The time-correlation function associated with

some particular process is in a sense the analog of the partition function

for equilibrium systems. Although both are difficult to evaluate exactly,

the appropriate properties of the system of interest can be formally

expressed in terms of these functions, and they serve as basic starting

points for computationally convenient approximations. Before the

development of the time-correlation function formalism, there was no single

unifying approach to nonequilibrium statistical mechanics such as Gibbs had

given to equilibrium statistical mechanics.

Chapters 21 and 22, two long chapters, introduce the time-correlation

function approach. We have chosen to introduce the time-correlation

function formalism through the absorption of electromagnetic radiation by a

system of molecules since the application is of general interest and the

derivation of the key formulas is quite pedagogical and requires no special

techniques. After presenting a similar application to light scattering, we

then develop the formalism in a more general way and apply the general

formalism to dielectric relaxation, thermal transport, neutron scattering,

light scattering, and several others.

Eleven appendixes are also included to supplement the textual material.

The intention here is to present a readable introduction to the topics

covered rather than a rigorous, formal development. In addition, a great

number of problems is included at the end of each chapter in order either to

increase the student’s understanding of the material or to introduce him or

her to selected extensions.

As this printing goes to press, we are beginning to plan a new edition of *Statistical Mechanics*. We would be grateful for any and all feedback from

loyal users intended to help us shape the next edition of this text.