The Statistical Foundations of Entropy

This book presents an innovative unified approach to the statistical foundations of entropy and the fundamentals of equilibrium statistical mechanics. These intimately related subjects are often developed in a fragmented historical manner which obscures the essential simplicity of their logical structure. In contrast, this book critically reassesses and systematically reorganizes the basic concepts into a simpler sequential framework which reveals more clearly their logical relationships. The inherent indistinguishability of identical particles is emphasized, and the resulting unification of classical and quantum statistics is discussed in detail.

The discussion is focused entirely on fundamental concepts, so applications are omitted. The book is written at the advanced undergraduate or beginning graduate level, and will be useful as a concise supplement to conventional books and courses in statistical mechanics, thermal physics, and thermodynamics. It is also suitable for self-study by those seeking a deeper and more detailed analysis of the fundamentals.

Contents:

• Introduction
• Fundamentals
• The Hypothesis of Equal a priori Probabilities
• Constraints
• The Principle of Maximum Entropy
• Thermodynamic Systems
• The Canonical and Grand Canonical Probability Distributions
• Many-Particle Systems
• Identical Particles are Inherently Indistinguishable

Readership: Advanced undergraduate and graduate students, and researchers in statistical physics.
Key Features:

• The sequential logical structure of the treatment, in which each level naturally follows from and builds upon the previous levels; concepts are not introduced until they are needed
• Despite brevity (made possible by omitting applications), the fundamental concepts are discussed in greater depth, detail, and generality than is usual in much larger and more expensive books
• Discusses and explains in detail the inherent indistinguishability of identical particles in both classical and quantum mechanics, correcting the misconception to the contrary widespread in most other books, thus unifying classical and quantum statistics within a single general framework