Statistical Mechanics

Donald A. McQuarrie
University of California, Davis


Preface

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.
 

Donald A. McQuarrie
March 2000
mquarrie@mcn.org