Physics

Statistical Mechanics by Donald A. McQuarrie (University Science Books) 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 chaptèrs, 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 Chap-ter 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 Boltz-mann 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 proper-ties 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 process-es 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.

Statistical mechanics is that branch of physics which studies macroscopic systems from a microscopic or molecular point of view. The goal of statistical mechanics is the understanding and prediction of macroscopic phenomena and the calculation of macroscopic properties from the properties of the individual molecules making up the system.

Present-day research in statistical mechanics varies from mathematically sophisticated discussions of general theorems to almost empirical calculations based upon simple, but nevertheless useful, molecular models. An example of the first type of research is the investigation of the question of whether statistical mechanics, as it is formulated today, is even capable of predicting the existence of a first-order phase transition. General questions of this kind are by their nature mathematically involved and are generally beyond the level of this book. We shall, however, discuss such questions to some extent later on. On the other hand, for many scientists statistical mechanics merely provides a recipe or prescription which allows them to calculate the properties of the physical systems which they are studying.

The techniques of statistical mechanics have been used in attacking a wide variety of physical problems. A quick glance through this text will show that statistical mechanics has been applied to gases, liquids, solutions, electrolytic solutions, polymers, adsorption, metals, spectroscopy, transport theory, the helix-coil transition of DNA, the electrical properties of matter, and cell membranes, among others.

Statistical mechanics may be broadly classified into two parts, one dealing with systems in equilibrium and the other with systems not in equilibrium. The treatment of systems in equilibrium is usually referred to as statistical thermodynamics, since it forms a bridge between thermodynamics (often called classical thermodynamics) and molecular physics.

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