Entropy Divergence And Majorization In Classical And Quantum Thermodynamics

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Entropy, Divergence, and Majorization in Classical and Quantum Thermodynamics

Takahiro Sagawa
Entropy Divergence and Majorization in Classical and Quantum Thermodynamics Book PDF

Author : Takahiro Sagawa
Publisher : Springer Nature
Page : 150 pages
File Size : 53,9 Mb
Release : 2022-03-23
Category : Science
ISBN : 9789811666445

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Entropy, Divergence, and Majorization in Classical and Quantum Thermodynamics by Takahiro Sagawa Pdf

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

Jochen Gemmer,M. Michel,Günter Mahler
Quantum Thermodynamics Book PDF

Author : Jochen Gemmer,M. Michel,Günter Mahler
Publisher : Springer
Page : 338 pages
File Size : 40,5 Mb
Release : 2009-07-14
Category : Science
ISBN : 9783540705109

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Quantum Thermodynamics by Jochen Gemmer,M. Michel,Günter Mahler Pdf

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.

Thermodynamics And Statistical Mechanics

Richard Fitzpatrick
Thermodynamics And Statistical Mechanics Book PDF

Author : Richard Fitzpatrick
Publisher : World Scientific
Page : 358 pages
File Size : 52,6 Mb
Release : 2020-07-07
Category : Science
ISBN : 9789811223372

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Thermodynamics And Statistical Mechanics by Richard Fitzpatrick Pdf

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.

Entropy Beyond the Second Law

Phil Attard
Entropy Beyond the Second Law Book PDF

Author : Phil Attard
Publisher : Unknown
Page : 0 pages
File Size : 55,5 Mb
Release : 2018
Category : Entropy
ISBN : 075031589X

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Entropy Beyond the Second Law by Phil Attard Pdf

"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.

Quantum Entropy and Its Use

M. Ohya,Denes Petz
Quantum Entropy and Its Use Book PDF

Author : M. Ohya,Denes Petz
Publisher : Springer Science & Business Media
Page : 368 pages
File Size : 40,7 Mb
Release : 2004-03-24
Category : Science
ISBN : 3540208062

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Quantum Entropy and Its Use by M. Ohya,Denes Petz Pdf

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.

Entropy in Foundations of Quantum Physics

Marcin Pawłowski
Entropy in Foundations of Quantum Physics Book PDF

Author : Marcin Pawłowski
Publisher : MDPI
Page : 266 pages
File Size : 52,9 Mb
Release : 2020-12-15
Category : Computers
ISBN : 9783039289516

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Entropy in Foundations of Quantum Physics by Marcin Pawłowski Pdf

This book is a collection of outstanding papers on various aspects of entropy at the foundation of quantum physics. The covered topics range from purely foundational issues such as contextuality and Bell and Leggett–Garg inequalities to applications such as quantum key distribution, teleportation, and image encoding. The main ingredient binding them together in this book is that in all of the contained papers, entropy plays a key role either as a mathematical tool or as a link which bridges the gap between different fields of science.

Fluctuation Relations and Nonequilibrium Thermodynamics in Classical and Quantum Systems

Gabriele De Chiara
Fluctuation Relations and Nonequilibrium Thermodynamics in Classical and Quantum Systems Book PDF

Author : Gabriele De Chiara
Publisher : Unknown
Page : 158 pages
File Size : 42,8 Mb
Release : 2020
Category : Electronic
ISBN : 3039369997

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Fluctuation Relations and Nonequilibrium Thermodynamics in Classical and Quantum Systems by Gabriele De Chiara Pdf

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

John D Ramshaw
The Statistical Foundations Of Entropy Book PDF

Author : John D Ramshaw
Publisher : World Scientific
Page : 216 pages
File Size : 44,8 Mb
Release : 2017-11-24
Category : Science
ISBN : 9789813234147

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The Statistical Foundations Of Entropy by John D Ramshaw Pdf

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.

Complexity, Entropy And The Physics Of Information

Wojciech H. Zurek
Complexity Entropy And The Physics Of Information Book PDF

Author : Wojciech H. Zurek
Publisher : CRC Press
Page : 548 pages
File Size : 48,8 Mb
Release : 2018-03-08
Category : Science
ISBN : 9780429982514

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Complexity, Entropy And The Physics Of Information by Wojciech H. Zurek Pdf

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.

Quantum Thermodynamics

Sebastian Deffner,Steve Campbell
Quantum Thermodynamics Book PDF

Author : Sebastian Deffner,Steve Campbell
Publisher : Morgan & Claypool Publishers
Page : 132 pages
File Size : 48,6 Mb
Release : 2019-07-02
Category : Science
ISBN : 9781643276588

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Quantum Thermodynamics by Sebastian Deffner,Steve Campbell Pdf

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

Andreas Greven,Gerhard Keller,Gerald Warnecke
Entropy Book PDF

Author : Andreas Greven,Gerhard Keller,Gerald Warnecke
Publisher : Princeton University Press
Page : 376 pages
File Size : 51,8 Mb
Release : 2014-09-08
Category : Mathematics
ISBN : 9781400865222

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Entropy by Andreas Greven,Gerhard Keller,Gerald Warnecke Pdf

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.

Entropy and Entropy Generation

J.S. Shiner
Entropy and Entropy Generation Book PDF

Author : J.S. Shiner
Publisher : Springer Science & Business Media
Page : 246 pages
File Size : 45,6 Mb
Release : 2006-04-11
Category : Science
ISBN : 9780306469329

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Entropy and Entropy Generation by J.S. Shiner Pdf

Entropy and entropy generation play essential roles in our understanding of many diverse phenomena ranging from cosmology to biology. Their importance is manifest in areas of immediate practical interest such as the provision of global energy as well as in others of a more fundamental flavour such as the source of order and complexity in nature. They also form the basis of most modern formulations of both equilibrium and nonequilibrium thermodynamics. Today much progress is being made in our understanding of entropy and entropy generation in both fundamental aspects and application to concrete problems. The purpose of this volume is to present some of these recent and important results in a manner that not only appeals to the entropy specialist but also makes them accessible to the nonspecialist looking for an overview of the field. This book contains fourteen contributions by leading scientists in their fields. The content covers such topics as quantum thermodynamics, nonlinear processes, gravitational and irreversible thermodynamics, the thermodynamics of Taylor dispersion, higher order transport, the mesoscopic theory of liquid crystals, simulated annealing, information and biological aspects, global energy, photovoltaics, heat and mass transport and nonlinear electrochemical systems. Audience: This work will be of value to physicists, chemists, biologists and engineers interested in the theory and applications of entropy and its generation.

Quantum Entropy and Its Use

M. Ohya,Denes Petz
Quantum Entropy and Its Use Book PDF

Author : M. Ohya,Denes Petz
Publisher : Springer
Page : 0 pages
File Size : 42,7 Mb
Release : 2004-04-06
Category : Science
ISBN : 3642579973

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Quantum Entropy and Its Use by M. Ohya,Denes Petz Pdf

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.

Entropy and the Time Evolution of Macroscopic Systems

Walter T. Grandy Jr.
Entropy and the Time Evolution of Macroscopic Systems Book PDF

Author : Walter T. Grandy Jr.
Publisher : OUP Oxford
Page : 225 pages
File Size : 42,5 Mb
Release : 2008-06-26
Category : Science
ISBN : 9780191562952

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Entropy and the Time Evolution of Macroscopic Systems by Walter T. Grandy Jr. Pdf

This book is based on the premise that the entropy concept, a fundamental element of probability theory as logic, governs all of thermal physics, both equilibrium and nonequilibrium. The variational algorithm of J. Willard Gibbs, dating from the 19th Century and extended considerably over the following 100 years, is shown to be the governing feature over the entire range of thermal phenomena, such that only the nature of the macroscopic constraints changes. Beginning with a short history of the development of the entropy concept by Rudolph Clausius and his predecessors, along with the formalization of classical thermodynamics by Gibbs, the first part of the book describes the quest to uncover the meaning of thermodynamic entropy, which leads to its relationship with probability and information as first envisioned by Ludwig Boltzmann. Recognition of entropy first of all as a fundamental element of probability theory in mid-twentieth Century led to deep insights into both statistical mechanics and thermodynamics, the details of which are presented here in several chapters. The later chapters extend these ideas to nonequilibrium statistical mechanics in an unambiguous manner, thereby exhibiting the overall unifying role of the entropy.

Entropy And Its Physical Meaning

J. S. Dugdale
Entropy And Its Physical Meaning Book PDF

Author : J. S. Dugdale
Publisher : CRC Press
Page : 209 pages
File Size : 44,9 Mb
Release : 2018-10-08
Category : Science
ISBN : 9781482272864

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Entropy And Its Physical Meaning by J. S. Dugdale Pdf

This text gives students a clear and easily understood introduction to entropy - a central concept in thermodynamics, but one which is often regarded as the most difficult to grasp. Professor Dugdale first presents a classical and historical view of entropy, looking in detail at the scientists who developed the concept, and at how they arrived at their ideas. This is followed by a statistical treatment which provides a more physical portrait of entropy, relating it to disorder and showing how physical and chemical systems tend to states of order at low temperatures. Dugdale includes here a brief account of some of the more intriguing manifestations of order in properties such as superconductivity and superfluidity.Entropy and Its Physical Meaning also includes a number of exercises which can be used for both self- learning and class work. It is intended to provide a complete understanding of the concept of entropy, making it valuable reading for undergraduates in physics, physical sciences and engineering, and for students studying thermodynamics within other science courses such as meteorology, biology and medicine.