Entropy Divergence And Majorization In Classical And Quantum Thermodynamics
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Entropy Divergence And Majorization In Classical And Quantum Thermodynamics
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Author : Takahiro Sagawa
language : en
Publisher: Springer Nature
Release Date : 2022-03-23
Entropy Divergence And Majorization In Classical And Quantum Thermodynamics written by Takahiro Sagawa and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-23 with Science categories.
Rich information-theoretic structure in out-of-equilibrium thermodynamics exists in both the classical and quantum regimes, leading to the fruitful interplay among statistical physics, quantum information theory, and mathematical theories such as matrix analysis and asymptotic probability theory. The main purpose of this book is to clarify how information theory works behind thermodynamics and to shed modern light on it. The book focuses on both purely information-theoretic concepts and their physical implications. From the mathematical point of view, rigorous proofs of fundamental properties of entropies, divergences, and majorization are presented in a self-contained manner. From the physics perspective, modern formulations of thermodynamics are discussed, with a focus on stochastic thermodynamics and resource theory of thermodynamics. In particular, resource theory is a recently developed field as a branch of quantum information theory to quantify “useful resources” and has an intrinsic connection to various fundamental ideas of mathematics and information theory. This book serves as a concise introduction to important ingredients of the information-theoretic formulation of thermodynamics.
Quantum Thermodynamics
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Author : Jochen Gemmer
language : en
Publisher: Springer
Release Date : 2009-07-14
Quantum Thermodynamics written by Jochen Gemmer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-14 with Science categories.
Over the years enormous effort was invested in proving ergodicity, but for a number of reasons, con?dence in the fruitfulness of this approach has waned. — Y. Ben-Menahem and I. Pitowsky [1] Abstract The basic motivation behind the present text is threefold: To give a new explanation for the emergence of thermodynamics, to investigate the interplay between quantum mechanics and thermodynamics, and to explore possible ext- sions of the common validity range of thermodynamics. Originally, thermodynamics has been a purely phenomenological science. Early s- entists (Galileo, Santorio, Celsius, Fahrenheit) tried to give de?nitions for quantities which were intuitively obvious to the observer, like pressure or temperature, and studied their interconnections. The idea that these phenomena might be linked to other ?elds of physics, like classical mechanics, e.g., was not common in those days. Such a connection was basically introduced when Joule calculated the heat equ- alent in 1840 showing that heat was a form of energy, just like kinetic or potential energy in the theory of mechanics. At the end of the 19th century, when the atomic theory became popular, researchers began to think of a gas as a huge amount of bouncing balls inside a box.
Entropy Beyond The Second Law
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Author : Phil Attard
language : en
Publisher:
Release Date : 2018
Entropy Beyond The Second Law written by Phil Attard and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Entropy categories.
"Entropy Beyond the Second Law presents a coherent formulation of all aspects of thermodynamics and statistical mechanics with entropy as the unifying theme. This includes formulating equilibrium theory and explaining the role of the Second Law in establishing the equilibrium state. It also establishes the foundations of non-equilibrium theory by generalizing the concept of entropy in an appropriate way. Finally, it addresses the relationship between classical and quantum statistical mechanics by invoking the collapse of the wave function into entropy states. A secondary purpose is to increase the understanding of entropy and the Second Law, and to correct misapprehensions and errors that have arisen over the years." -- Prové de l'editor.
Thermodynamics And Statistical Mechanics
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Author : Richard Fitzpatrick
language : en
Publisher: World Scientific
Release Date : 2020-07-07
Thermodynamics And Statistical Mechanics written by Richard Fitzpatrick and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-07 with Science categories.
This book provides a comprehensive exposition of the theory of equilibrium thermodynamics and statistical mechanics at a level suitable for well-prepared undergraduate students. The fundamental message of the book is that all results in equilibrium thermodynamics and statistical mechanics follow from a single unprovable axiom — namely, the principle of equal a priori probabilities — combined with elementary probability theory, elementary classical mechanics, and elementary quantum mechanics.
Quantum Entropy And Its Use
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Author : M. Ohya
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-03-24
Quantum Entropy And Its Use written by M. Ohya and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-24 with Science categories.
Numerous fundamental properties of quantum information measurement are developed, including the von Neumann entropy of a statistical operator and its limiting normalized version, the entropy rate. Use of quantum-entropy quantities is made in perturbation theory, central limit theorems, thermodynamics of spin systems, entropic uncertainty relations, and optical communication. This new softcover corrected reprint contains summaries of recent developments added to the ends of the chapters.
Fluctuation Relations And Nonequilibrium Thermodynamics In Classical And Quantum Systems
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Author : Gabriele de Chiara
language : en
Publisher:
Release Date : 2020-09-04
Fluctuation Relations And Nonequilibrium Thermodynamics In Classical And Quantum Systems written by Gabriele de Chiara and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-04 with categories.
This Special Issue contains novel results in the area of out-of-equilibrium classical and quantum thermodynamics. Contributions are from different areas of physics, including statistical mechanics, quantum information and many-body systems.
The Statistical Foundations Of Entropy
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Author : John D Ramshaw
language : en
Publisher: World Scientific
Release Date : 2017-11-24
The Statistical Foundations Of Entropy written by John D Ramshaw and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-24 with Science categories.
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.
Quantum Thermodynamics
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Author : Sebastian Deffner
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2019-07-02
Quantum Thermodynamics written by Sebastian Deffner and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-02 with Science categories.
This book provides an introduction to the emerging field of quantum thermodynamics, with particular focus on its relation to quantum information and its implications for quantum computers and next generation quantum technologies. The text, aimed at graduate level physics students with a working knowledge of quantum mechanics and statistical physics, provides a brief overview of the development of classical thermodynamics and its quantum formulation in Chapter 1. Chapter 2 then explores typical thermodynamic settings, such as cycles and work extraction protocols, when the working material is genuinely quantum. Finally, Chapter 3 explores the thermodynamics of quantum information processing and introduces the reader to some more state of-the-art topics in this exciting and rapidly developing research field.
Entropy
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Author : Andreas Greven
language : en
Publisher: Princeton University Press
Release Date : 2014-09-08
Entropy written by Andreas Greven and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-08 with Mathematics categories.
The concept of entropy arose in the physical sciences during the nineteenth century, particularly in thermodynamics and statistical physics, as a measure of the equilibria and evolution of thermodynamic systems. Two main views developed: the macroscopic view formulated originally by Carnot, Clausius, Gibbs, Planck, and Caratheodory and the microscopic approach associated with Boltzmann and Maxwell. Since then both approaches have made possible deep insights into the nature and behavior of thermodynamic and other microscopically unpredictable processes. However, the mathematical tools used have later developed independently of their original physical background and have led to a plethora of methods and differing conventions. The aim of this book is to identify the unifying threads by providing surveys of the uses and concepts of entropy in diverse areas of mathematics and the physical sciences. Two major threads, emphasized throughout the book, are variational principles and Ljapunov functionals. The book starts by providing basic concepts and terminology, illustrated by examples from both the macroscopic and microscopic lines of thought. In-depth surveys covering the macroscopic, microscopic and probabilistic approaches follow. Part I gives a basic introduction from the views of thermodynamics and probability theory. Part II collects surveys that look at the macroscopic approach of continuum mechanics and physics. Part III deals with the microscopic approach exposing the role of entropy as a concept in probability theory, namely in the analysis of the large time behavior of stochastic processes and in the study of qualitative properties of models in statistical physics. Finally in Part IV applications in dynamical systems, ergodic and information theory are presented. The chapters were written to provide as cohesive an account as possible, making the book accessible to a wide range of graduate students and researchers. Any scientist dealing with systems that exhibit entropy will find the book an invaluable aid to their understanding.
Complexity Entropy And The Physics Of Information
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Author : Wojciech H. Zurek
language : en
Publisher: CRC Press
Release Date : 2018-03-08
Complexity Entropy And The Physics Of Information written by Wojciech H. Zurek and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-08 with Science categories.
This book has emerged from a meeting held during the week of May 29 to June 2, 1989, at St. John’s College in Santa Fe under the auspices of the Santa Fe Institute. The (approximately 40) official participants as well as equally numerous “groupies” were enticed to Santa Fe by the above “manifesto.” The book—like the “Complexity, Entropy and the Physics of Information” meeting explores not only the connections between quantum and classical physics, information and its transfer, computation, and their significance for the formulation of physical theories, but it also considers the origins and evolution of the information-processing entities, their complexity, and the manner in which they analyze their perceptions to form models of the Universe. As a result, the contributions can be divided into distinct sections only with some difficulty. Indeed, I regard this degree of overlapping as a measure of the success of the meeting. It signifies consensus about the important questions and on the anticipated answers: they presumably lie somewhere in the “border territory,” where information, physics, complexity, quantum, and computation all meet.
