Yoshioka Daijiro. Statistical Physics: An Introduction

Textbook. — Berlin—Heidelberg—N.Y.: Springer, 2007. — XII + 208 p.: ill. — ISBN13: 978-3-540-28605-9.A macroscopic system consists of a tremendous number of microscopic atoms and molecules. In thermal equilibrium the state of such a system is uniquely defined, despite the fact that the microscopic particles behave quite randomly. This observation gives rise to the fundamental law of the statistical physics; it allows entropy to be defined and a framework for the theory to be constructed but cannot be derived form quantum mechanics or force laws. Introduction to Statistical Physics seeks to explain the laws of the macroscopic level to undergraduate students learning them for the first time. The first part of this book explains the essence of statistical physics without going into details such as Liouville’s theorem or ergodic theorem, which are difficult for beginners and unnecessary for actual application of the statistical mechanics. In the second part, statistical mechanics ís applied to various systems which look different but have the same mathematical structure, in particular, features applications to quantum dynamics, thermodynamics, Ising model and statistical dynamics of free spins. Advanced topics in phase transitions and dense gases conclude the text, plus helpful appendices.General Principles
Thermal Equilibrium and the Principle of Equal Probability
Entropy
The Partition Function and the Free Energy
Elementary Applications
IdealGases
The Heat Capacity of a Solid, and Black-Body Radiation
The Elasticity of Rubber
Magnetic Materials
More Advanced Topics
First-Order Phase Transitions
Second-Order Phase Transitions
Dense Gases — Ideal Gases at Low Temperature
Appendices
Formulas Related to the Factorial Function
The Gaussian Distribution Function
Lagrange’s Method of Undetermined Multipliers
Volume of a Hypersphere
Hyperbolic Functions
Boundary Conditions
The Riemann Zeta Function
References
Index