Entropy, Divergence, and Majorization in Classical and Quantum Thermodynamics

Out-of-equilibrium thermodynamics has a rich information-theoretic structure in both the classical and quantum regimes, leading to the interplay between statistical physics, quantum information theory, and mathematical theories. This book aims to clarify how information theory works behind thermodynamics and shed modern light on it, focusing on both information-theoretic concepts and their physical implications. It provides rigorous proofs of fundamental properties of entropies, divergences, and majorization and discusses modern formulations of thermodynamics, including stochastic thermodynamics and resource theory of thermodynamics.

Format: Paperback / softback
Length: 149 pages
Publication date: 23 March 2022
Publisher: Springer Verlag, Singapore

In the realm of out-of-equilibrium thermodynamics, a rich information-theoretic structure emerges across both the classical and quantum regimes, fostering a vibrant interplay among statistical physics, quantum information theory, and mathematical frameworks such as matrix analysis and asymptotic probability theory. The primary objective of this book is to elucidate the intricate workings of information theory within the context of thermodynamics, offering a contemporary perspective on this fundamental discipline. The book delves into both purely information-theoretic concepts and their tangible physical implications, providing a comprehensive exploration. From a mathematical standpoint, rigorous proofs of fundamental properties of entropies, divergences, and majorization are presented in a self-contained manner, ensuring a clear understanding of these key concepts. On the physics front, modern formulations of thermodynamics are discussed, with a particular emphasis on stochastic thermodynamics and resource theory of thermodynamics. Resource theory, in particular, emerges as a recently developed field, serving as a branch of quantum information theory, dedicated to quantifying "useful resources." This field possesses an intrinsic connection to various fundamental ideas of mathematics and information theory, making it a valuable tool for understanding thermodynamic systems. This book serves as a concise introduction to the essential ingredients of the information-theoretic formulation of thermodynamics, offering a valuable resource for scholars and researchers in the field.

Weight: 266g
Dimension: 156 x 235 x 14 (mm)
ISBN-13: 9789811666438
Edition number: 1st ed. 2022