Introduction to Modern Statistical Mechanics
Book Preface
This book presents the material I use in my lectures on elementary statistical mechanics, a onesemester course I have taught at the University of Illinois and at the University of Pennsylvania. Students enter this course with some knowledge of thermodynamics, the Boltzmann distribution law, and simple quantum mechanics, usually acquired from undergraduate physical chemistry or modern physics at the level of Moore’s Physical Chemistry. The purpose of my lectures is not only to give the students a deeper understanding of thermodynamics and the principles of equilibrium statistical mechanics, but also to introduce them to the modern topics of Monte Carlo sampling, the renormalization group theory, and the fluctuationdissipation theorem. The ideas surrounding these topics have revolutionized the subject of statistical mechanics, and it is largely due to them that the practitioners of statistical mechanics now play a significant role in the current research and discoveries of fields ranging from molecular biology to material science and engineering, to chemical structure and dynamics, and even to high energy particle physics. Thus, in my opinion, no serious student of the natural sciences is properly educated without some understanding of these modern topics and concepts such as “order parameters and ” correlation functions/’ It is also my opinion and experience that these topics and concepts can and should be covered in a onesemester introductory course.
To cover this material at an introductory level, I make frequent use of simplified models. In this way, I can keep the mathematics relatively simple yet still describe many of the sophisticated ideas in the field. I refrain from treating advanced theoretical techniques (e.g., diagrammatic and field theoretic methods) even though these are among my favorite topics for research. I also treat only briefly the traditional statistical thermodynamics subjects of ideal gases and gas phase chemical equilibria. In the former case, this book should provide necessary background for the interested student to pursue advanced courses or readings in manybody theory. In the latter case, since there are already so many excellent texts devoted to these topics, it is wastefully redundant to spend much time on them here. Furthermore, these subjects have now become rather standard in the materials presented in undergraduate physical chemistry courses
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May 30, 2020 
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