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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.
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.
John von Neumann and the Foundations of Quantum Physics by Miklós Rédei,Michael Stöltzner Pdf
John von Neumann (1903-1957) was undoubtedly one of the scientific geniuses of the 20th century. The main fields to which he contributed include various disciplines of pure and applied mathematics, mathematical and theoretical physics, logic, theoretical computer science, and computer architecture. Von Neumann was also actively involved in politics and science management and he had a major impact on US government decisions during, and especially after, the Second World War. There exist several popular books on his personality and various collections focusing on his achievements in mathematics, computer science, and economy. Strangely enough, to date no detailed appraisal of his seminal contributions to the mathematical foundations of quantum physics has appeared. Von Neumann's theory of measurement and his critique of hidden variables became the touchstone of most debates in the foundations of quantum mechanics. Today, his name also figures most prominently in the mathematically rigorous branches of contemporary quantum mechanics of large systems and quantum field theory. And finally - as one of his last lectures, published in this volume for the first time, shows - he considered the relation of quantum logic and quantum mechanical probability as his most important problem for the second half of the twentieth century. The present volume embraces both historical and systematic analyses of his methodology of mathematical physics, and of the various aspects of his work in the foundations of quantum physics, such as theory of measurement, quantum logic, and quantum mechanical entropy. The volume is rounded off by previously unpublished letters and lectures documenting von Neumann's thinking about quantum theory after his 1932 Mathematical Foundations of Quantum Mechanics. The general part of the Yearbook contains papers emerging from the Institute's annual lecture series and reviews of important publications of philosophy of science and its history.
Maximum Entropy, Information Without Probability and Complex Fractals by Guy Jumarie Pdf
Every thought is a throw of dice. Stephane Mallarme This book is the last one of a trilogy which reports a part of our research work over nearly thirty years (we discard our non-conventional results in automatic control theory and applications on the one hand, and fuzzy sets on the other), and its main key words are Information Theory, Entropy, Maximum Entropy Principle, Linguistics, Thermodynamics, Quantum Mechanics, Fractals, Fractional Brownian Motion, Stochastic Differential Equations of Order n, Stochastic Optimal Control, Computer Vision. Our obsession has been always the same: Shannon's information theory should play a basic role in the foundations of sciences, but subject to the condition that it be suitably generalized to allow us to deal with problems which are not necessarily related to communication engineering. With this objective in mind, two questions are of utmost importance: (i) How can we introduce meaning or significance of information in Shannon's information theory? (ii) How can we define and/or measure the amount of information involved in a form or a pattern without using a probabilistic scheme? It is obligatory to find suitable answers to these problems if we want to apply Shannon's theory to science with some chance of success. For instance, its use in biology has been very disappointing, for the very reason that the meaning of information is there of basic importance, and is not involved in this approach.
Holographic Entanglement Entropy by Mukund Rangamani,Tadashi Takayanagi Pdf
This book provides a comprehensive overview of developments in the field of holographic entanglement entropy. Within the context of the AdS/CFT correspondence, it is shown how quantum entanglement is computed by the area of certain extremal surfaces. The general lessons one can learn from this connection are drawn out for quantum field theories, many-body physics, and quantum gravity. An overview of the necessary background material is provided together with a flavor of the exciting open questions that are currently being discussed. The book is divided into four main parts. In the first part, the concept of entanglement, and methods for computing it, in quantum field theories is reviewed. In the second part, an overview of the AdS/CFT correspondence is given and the holographic entanglement entropy prescription is explained. In the third part, the time-dependence of entanglement entropy in out-of-equilibrium systems, and applications to many body physics are explored using holographic methods. The last part focuses on the connection between entanglement and geometry. Known constraints on the holographic map, as well as, elaboration of entanglement being a fundamental building block of geometry are explained. The book is a useful resource for researchers and graduate students interested in string theory and holography, condensed matter and quantum information, as it tries to connect these different subjects linked by the common theme of quantum entanglement.
The Biggest Ideas in the Universe 1 by Sean Carroll Pdf
THE NEW YORK TIMES BESTSELLER ‘Sean Carroll has achieved something I thought impossible: a bridge between popular science and the mathematical universe of working physicists. Magnificent!’ Brian Clegg, author of Ten Days in Physics that Shook the World Immense, strange and infinite, the world of modern physics often feels impenetrable to the undiscerning eye – a jumble of muons, gluons and quarks, impossible to explain without several degrees and a research position at CERN. But it doesn’t have to be this way! Allow world-renowned theoretical physicist and bestselling author Sean Carroll to guide you through the biggest ideas in the universe. Elegant and simple, Carroll unravels this web of theories and formulae equation by equation, getting to the heart of the truths they represent. — In Space, Time and Motion, the first book of this landmark trilogy, Carroll delves into the core of classical physics. From Euclid to Einstein, Space, Time and Motion explores the ideas which revolutionised science and forever changed our understanding of our place in the cosmos.
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.
"The Disordered Universe - Exploring the Concept of Entropy" takes readers on a captivating journey into the intricate realm of entropy. From the microscopic world of quantum mechanics to the grand scale of cosmology, this book unravels the profound influence of entropy in shaping the behavior of our universe. With clarity and depth, it delves into the interplay between chaos and order, revealing how entropy drives adaptation, innovation, and the emergence of complexity. Engaging and enlightening, this book illuminates the fundamental role of entropy and its applications across various scientific fields and everyday life.
Geometry Of Quantum Potential, The: Entropic Information Of The Vacuum by Fiscaletti Davide Pdf
In virtue of its features, Bohm's quantum potential introduces interesting and relevant perspectives towards a satisfactory geometrodynamic description of quantum processes. This book makes a comprehensive state-of-the-art review of some of the most significant elements and results about the geometrodynamic picture determined by the quantum potential in various contexts. Above all, the book explores the perspectives about the fundamental arena subtended by the quantum potential, the link between the geometry associated to the quantum potential and a fundamental quantum vacuum. After an analysis of the geometry subtended by the quantum potential in the different fields of quantum physics (the non-relativistic domain, the relativistic domain, the relativistic quantum field theory, the quantum gravity domain and the canonical quantum cosmology), in the second part of the book, a recent interpretation of Bohm's quantum potential in terms of a more fundamental entity called quantum entropy, the approach of the symmetryzed quantum potential and the link between quantum potential and quantum vacuum are analysed, also in the light of the results obtained by the author. Contents: Introduction The Geometry of the Quantum Potential in Different Contexts Quantum Entropy and Quantum Potential Immediate Quantum Information and Symmetryzed Quantum Potential The Quantum Potential ... and the Quantum Vacuum Conclusions References Index Readership: Researchers interested in the link between the geometrodynamic action of the quantum potential and a fundamental quantum vacuum, in the different contexts of quantum physics. Keywords: Entropy;Quantum;Potential;Symmetry;Geometry;GeometrodynamicReview: Key Features: This book provides a complete guide to the geometrodynamic features of the quantum potential as key of reading and understanding of the different fields of quantum physics To explore relevant perspectives about the fundamental arena of quantum processes which determines the action of the quantum potential and its geometry This book introduces, in the light of relevant current research, interesting and novel perspectives as regards the link between the geometrodynamic action of the quantum potential and a fundamental quantum vacuum, in the different contexts of quantum physics
Dynamics, Information and Complexity in Quantum Systems by Fabio Benatti Pdf
This second edition of Dynamics, Information and Complexity in Quantum Systems widens its scope by focussing more on the dynamics of quantum correlations and information in microscopic and mesoscopic systems, and their use for metrological and machine learning purposes. The book is divided into three parts: Part One: Classical Dynamical Systems Addresses classical dynamical systems, classical dynamical entropy, and classical algorithmic complexity. Includes a survey of the theory of simple perceptrons and their storage capacity. Part Two: Quantum Dynamical Systems Focuses on the dynamics of entanglement under dissipative dynamics and its metrological use in finite level quantum systems. Discusses the quantum fluctuation approach to large-scale mesoscopic systems and their emergent dynamics in quantum systems with infinitely many degrees of freedom. Introduces a model of quantum perceptron whose storage capacity is computed and compared with the classical one. Part Three: Quantum Dynamical Entropies and Complexities Devoted to quantum dynamical entropies and algorithmic complexities. This book is meant for advanced students, young and senior researchers working in the fields of quantum statistical mechanics, quantum information, and quantum dynamical systems. It is self-contained, and the only prerequisites needed are a standard knowledge of statistical mechanics, quantum mechanics, and linear operators on Hilbert spaces.
A Quantum Leap In Information Theory by Stefano Mancini,Andreas Winter Pdf
This is an introductory textbook at graduate or advanced undergraduate level. Students with diverse backgrounds, in mathematics, physics and computer science, can use it to become acquainted with the quantum theory of information. Its scope is deliberately chosen to be not too broad, while being self-consistent and usable for a semester-long course for beginners. The subject is presented using a balanced mix of intuitive arguments and rigorous formalism. The emphasis is not on the physical information but rather in the formal and mathematical features of quantum information theory. Only a basic knowledge of algebra is required to understand the contents of this book. In particular, a background in quantum mechanics is not needed, since quantum theory is used as a mere mathematical framework without entering into physical interpretations.The book introduces all necessary concepts from quantum theory and classical information theory, to cover the elements of quantum Shannon theory: quantum states and channels, data compression and entropy, error correcting codes and channel capacities, as well as the basics of entanglement theory and quantum cryptography.Examples are provided to help the reader in understanding the different concepts, together with exercises at the end of each chapter.
Statistical Mechanics And Scientific Explanation: Determinism, Indeterminism And Laws Of Nature by Valia Allori Pdf
The book explores several open questions in the philosophy and the foundations of statistical mechanics. Each chapter is written by a leading expert in philosophy of physics and/or mathematical physics. Here is a list of questions that are addressed in the book:
Quantum Systems, Channels, Information by Alexander S. Holevo Pdf
The main emphasis of this work is the mathematical theory of quantum channels and their entropic and information characteristics. Quantum information theory is one of the key research areas, since it leads the way to vastly increased computing speeds by using quantum systems to store and process information. Quantum cryptography allows for secure communication of classified information. Research in the field of quantum informatics, including quantum information theory, is in progress in leading scientific centers throughout the world. The past years were marked with impressive progress made by several researchers in solution of some difficult problems, in particular, the additivity of the entropy characteristics of quantum channels. This suggests a need for a book that not only introduces the basic concepts of quantum information theory, but also presents in detail some of the latest achievements.
