This book presents a thorough discussion of the role of entropy in thermodynamic systems, with particular emphasis on its influence on the stability of matter. Challenging conventional energy-centric paradigms, the book explores how entropy leads to stable phases in systems, especially systems characterized by frustration.

Through detailed explanations of key concepts of entropy, and concrete examples, such as entropic forces, adiabatic demagnetization, and entropy-driven phase transitions, the book elucidates the multifaceted nature of entropy.

Special attention is given to the phenomenon of "order by disorder" in frustrated systems, where entropy plays a crucial role in determining thermodynamic stability. Both discrete and continuous spin systems are analyzed to illustrate the mechanisms by which entropy governs ordering processes. The treatment also extends to quantum fluctuations and their contribution to phase transitions, offering a comprehensive perspective across classical and quantum regimes. Extension of entropy to non-equilibrium states and also to non-extensive states is also explained.

Intended for researchers and graduate and advanced undergraduate students in physics and related disciplines, this volume offers a detailed explanation of the concept of entropy, giving theoretical insights with illustrative case studies. It serves as a valuable resource for those who would like to more deeply understand entropy and its foundational role in the thermodynamics of complex systems.

Autorentext

Seiji Miyashita is an emeritus professor at The University of Tokyo. His work has been mainly involved in statistical physics and magnetism. He received his Doctor of Science from The University of Tokyo in 1981. He was an assistant professor at the General Education and Graduate School of Human and Environmental Studies, Kyoto University from 1988 to 1995, and was a professor at the Department of Earth and Space Science, Osaka University (currently the University of Osaka) from 1995 to1999. He moved to the Department of Applied Physics, The University of Tokyo, and then to the Department of Physics as a professor in 2005. He retired in 2020 and is now an emeritus professor of The University of Tokyo. He was also the editor- in-chief of the Journal of the Physical Society of Japan (JPSJ) from 2020 to 2024 and is the president of the Physical Society of Japan from 2025 to 2027. He was honored with the Inoue Prize for Science in 2001 and the Docteur Honoris Causa from the University of Versailles in 2011.