An Introduction to Disorder: Entropy, Information, and Morphologies

Disorder is everywhere - in alloys, in thermal fluctuations, and in the amorphous structures of glasses. Understanding it is essential to understanding real materials. This book offers an introduction to the physics of disordered systems, from their foundations in entropy and statistical mechanics to modern applications in information and quantum information theory. It begins discussing the generation and use of random numbers, Monte Carlo and quantum Monte Carlo methods, and impurity effects ranging from single‑atom substitutions to large‑scale defects such as dislocations and grain boundaries. Entropy is explored as a unifying concept linking statistical mechanics, information theory, and quantum information, including Shannon and von Neumann entropies and quantum entanglement. Further chapters examine amorphous materials, glasses and spin glasses, Anderson localization and metal–insulator transitions, as well as fractals and chaotic dynamics. It concludes with the impact of disorder on critical phenomena. Designed for advanced undergraduates and first‑year graduate students, this book serves as a comprehensive entry point into the study of disorder. It provides a solid conceptual foundation while pointing readers to key research literature for deeper exploration, making it both an accessible textbook and a valuable reference for future study. Throughout, the mathematics is kept as simple as possible, with more advanced methods introduced only when needed. Key features: Presents a basic introduction for advanced undergraduate and first year graduate students in physics and engineering, both theoretical and experimental. Covers topics of the most interest to researchers in nanotechnology, material science, statistical physics, information theory, and quantum information theory. Explores the variety of different types of disorder which are found in physical systems.