Über die Autorin bzw. den Autor

Harvey Gould is Professor of Physics at Clark University and Associate Editor of the American Journal of Physics. Jan Tobochnik is the Dow Distinguished Professor of Natural Science at Kalamazoo College and Editor of the American Journal of Physics. They are the coauthors, with Wolfgang Christian, of An Introduction to Computer Simulation Methods: Applications to Physical Systems.

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"In addition to being a clear, comprehensive introduction to the field, this book includes a unique and welcome feature: an emphasis on computer simulations. These are integral to the exposition and provide key insights into fundamental concepts that so often confuse newcomers to the field. Simulations also give students a tool to investigate interesting topics that are normally considered too advanced for undergraduates. I highly recommend this book to anyone planning to teach undergraduate statistical and thermal physics."--Jon Machta, University of Massachusetts Amherst

"This is an ambitious book written by two experienced researchers and teachers. Starting from the microscopic dynamics of atoms and molecules, it uses statistical mechanical ideas to explain the thermodynamic behavior of macroscopic systems, and amply illustrates these ideas using hands-on computer simulations. Both teachers and students will find this book stimulating and rewarding."--Joel L. Lebowitz, Rutgers University

"Gould and Tobochnik are respected researchers in the field and have a good sense of what is significant.Statistical and Thermal Physics includes many problems, exercises, and enlightening commentaries. The textbook places unique emphasis on numerical simulation techniques and what one can learn from them, and closely integrates them into the presentation. This is a welcome innovation."--Theodore L. Einstein, University of Maryland

"This is an excellent book. It is better than any other textbook I have encountered for an undergraduate course in statistical thermodynamics. The authors' use of simulations to build a student's intuition is novel, and the problems and examples are very useful. They bring out the important issues and are a real asset in getting students to think about the subject."--William Klein, Boston University

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Statistical and Thermal Physics

PRINCETON UNIVERSITY PRESS

Contents

Preface......................................................................................xi1 From Microscopic to Macroscopic Behavior...................................................12 Thermodynamic Concepts and Processes.......................................................323 Concepts of Probability....................................................................1114 The Methodology of Statistical Mechanics...................................................1805 Magnetic Systems...........................................................................2416 Many-Particle Systems......................................................................3087 The Chemical Potential and Phase Equilibria................................................3768 Classical Gases and Liquids................................................................4109 Critical Phenomena: Landau Theory and the Renormalization Group Method.....................459Appendix: Physical Constants and Mathematical Relations......................................495Index........................................................................................505

Chapter One

We explore the fundamental differences between microscopic and macroscopic systems, note that bouncing balls come to rest and hot objects cool, and discuss how the behavior of macroscopic systems is related to the behavior of their microscopic constituents. Computer simulations are introduced to demonstrate the general qualitative behavior of macroscopic systems.

1.1 Introduction

Our goal is to understand the properties of macroscopic systems, that is, systems of many electrons, atoms, molecules, photons, or other constituents. Examples of familiar macroscopic objects include systems such as the air in your room, a glass of water, a coin, and a rubber band-examples of a gas, liquid, solid, and polymer, respectively. Less familiar macroscopic systems include superconductors, cell membranes, the brain, the stock market, and neutron stars.

We will find that the type of questions we ask about macroscopic systems differ in important ways from the questions we ask about systems that we treat microscopically. For example, consider the air in your room. Have you ever wondered about the trajectory of a particular molecule in the air? Would knowing that trajectory be helpful in understanding the properties of air? Instead of questions such as these, examples of questions that we do ask about macroscopic systems include the following:

1. How does the pressure of a gas depend on the temperature and the volume of its container? 2. How does a refrigerator work? How can we make it more efficient? 3. How much energy do we need to add to a kettle of water to change it to steam? 4. Why are the properties of water different from those of steam, even though water and steam consist of the same type of molecules? 5. How and why does a liquid freeze into a particular crystalline structure? 6. Why does helium have a superfluid phase at very low temperatures? Why do some materials exhibit zero resistance to electrical current at sufficiently low temperatures? 7. In general, how do the properties of a system emerge from its constituents? 8. How fast does the current in a river have to be before its flow changes from laminar to turbulent? 9. What will the weather be tomorrow? These questions can be roughly classified into three groups. Questions 1-3 are concerned with macroscopic properties such as pressure, volume, and temperature and processes related to heating and work. These questions are relevant to thermodynamics, which provides a framework for relating the macroscopic properties of a system to one another. Thermodynamics is concerned only with macroscopic quantities and ignores the microscopic variables that characterize individual molecules. For example, we will find that understanding the maximum efficiency of a refrigerator does not require a knowledge of the particular liquid used as the coolant. Many of the applications of thermodynamics are to engines, for example, the internal combustion engine and the steam turbine.

Questions 4-7 relate to understanding the behavior of macroscopic systems starting from the atomic nature of matter. For example, we know that water consists of molecules of hydrogen and oxygen. We also know that the laws of classical and quantum mechanics determine the behavior of molecules at the microscopic level. The goal of statistical mechanics is to begin with the microscopic laws of physics that govern the behavior of the constituents of the system and deduce the properties of the system as a whole. Statistical mechanics is a bridge between the microscopic and macroscopic worlds.

Question 8 also relates to a macroscopic system, but temperature is not relevant in this case. Moreover, turbulent flow continually changes in time. Question 9 concerns macroscopic phenomena that change with time. Although there has been progress in our understanding of time-dependent phenomena such as turbulent flow and hurricanes, our understanding of such phenomena is much less advanced than our understanding of time-independent systems. For this reason we will focus our attention on systems whose macroscopic properties are independent of time and consider questions such as those in Questions 1-7.

1.2 Some Qualitative Observations

We begin our discussion of macroscopic systems by considering a glass of hot water. We know that, if we place a glass of hot water into a large cold room, the hot water cools until its temperature equals that of the room. This simple observation illustrates two important properties associated with macroscopic systems-the importance of temperature and the "arrow" of time. Temperature is familiar because it is associated with the physiological sensations of hot and cold and is important in our everyday experience.

The direction or arrow of time raises many questions. Have you ever observed a glass of water at room temperature spontaneously become hotter? Why not? What other phenomena exhibit a direction of time? The direction of time is expressed by the nursery rhyme:

Humpty Dumpty sat on a wall Humpty Dumpty had a great fall All the king's horses and all the king's men Couldn't put Humpty Dumpty back together again.

Is there a direction of time for a single particle? Newton's second law for a single particle, F = dp/dt, implies that the motion of particles is time-reversal invariant; that is, Newton's second law looks the same if the time t is replaced by -t and the momentum p by -p. There is no direction of time at the microscopic level. Yet if we drop a basketball onto a floor, we know that it will bounce and eventually come to rest. Nobody has observed a ball at rest spontaneously begin to bounce, and then bounce higher and higher. So based on simple everyday observations we can conclude that the behaviors of macroscopic bodies and single particles are very different.

Unlike scientists of about a century or so ago, we know that macroscopic systems such as a glass of water and a basketball...