Introduction To Entropy

This book considers a relatively new metric in complex systems, transfer entropy, derived from a series of measurements, usually a time series. After a qualitative introduction and a chapter that explains the key ideas from statistics required to understand the text, the authors then present information theory and transfer entropy in depth. A key feature of the approach is the authors' work to show the relationship between information flow and complexity. The later chapters demonstrate information transfer in canonical systems, and applications, for example in neuroscience and in finance. The book will be of value to advanced undergraduate and graduate students and researchers in the areas of computer science, neuroscience, physics, and engineering.

Entropy for Biologists: An Introduction to Thermodynamics is an introductory book for people in the life sciences who wish to master the concepts of thermal physics without being forced to a degree and rate of symbol manipulation which is foreign to their patterns of thought. The book opens with a chapter on temperature, followed by separate chapters that discuss the concepts of energy, kinetic theory, total energy, the second law of thermodynamics, entropy, and probability and information theory. Subsequent chapters deal with statistical mechanics and its relation to thermodynamics, free-energy functions, applications of the Gibbs free energy and the Gibbs chemical potential, and measurement in thermal physics. The book is primarily directed at those graduate and advanced undergraduate students of biology and biochemistry who wish to develop a sense of confidence about their understanding of the thermal physics which will be useful in pursuing their work. It may also prove useful to professionals who wish to bolster their knowledge in this area.

Striving to explore the subject in as simple a manner as possible, this book helps readers understand the elusive concept of entropy. Innovative aspects of the book include the construction of statistical entropy from desired properties, the derivation of the entropy of classical systems from purely classical assumptions, and a statistical thermodynamics approach to the ideal Fermi and ideal Bose gases. Derivations are worked through step-by-step and important applications are highlighted in over 20 worked examples. Around 50 end-of-chapter exercises test readers' understanding. The book also features a glossary giving definitions for all essential terms, a time line showing important developments, and list of books for further study. It is an ideal supplement to undergraduate courses in physics, engineering, chemistry and mathematics.

Statistical mechanics: the bane of many a physics student, and traditionally viewed as a long parade of ensembles, partition functions, and partial derivatives. But the subject needn't be arcane. When pared back to its underlying concepts and built from the ground up, statistical mechanics takes on a charm of its own, and sheds light on all manner of physical phenomena. This book presents a straightforward introduction to the key concepts in statistical mechanics, following the popular style of the author's highly successful textbook "Explorations in Mathematical Physics". Offering a clear, conceptual approach to the subject matter, the book presents a treatment that is mathematically complete, while remaining very accessible to undergraduates. It commences by asking: why does an ink drop spread out in a bathtub of water? This showcases the importance of counting configurations, which leads naturally to ideas of microstates, energy, entropy, thermodynamics, and physical chemistry. With this foundation, the Boltzmann distribution writes itself in its fullest form, and this opens the door to the Maxwell distribution and related areas of thermal conductivity and viscosity. Quantum ideas then appear: bosons via Einstein's and Debye's theories of heat capacity, and fermions via electrical conduction and low-temperature heat capacity of metals. The text ends with a detailed derivation of blackbody radiation, and uses this to discuss the greenhouse effect, lasers, and cosmology. Suitable for use with core undergraduate courses in statistical mechanics and thermodynamics, this book concentrates on using solid mathematics, while avoiding cumbersome notation. All the necessary mathematical steps are included in the body of the text and in the worked examples. Reviews of Explorations in Mathematical Physics by Don Koks, 2006 "With enjoyable and sometimes surprising excursions along the way, the journey provides a fresh look at many familiar topics, as it takes us from basic linear mathematics to general relativity... look forward to having your geometric intuition nourished and expanded by the author's intelligent commentaries." (Eugen Merzbacher, University of North Carolina) "... an interesting supplement to standard texts for teaching mathematical methods in physics, as it will add alternative views that could serve as additional material." (S. Marcelja, Australian Journal of Physics) "... a tour through the main ideas forming the language of modern mathematical physics ...it is a difficult task for the author to decide what is a good balance between the topics and their presentation, but in this case it has been achieved. ...for those physicists who would like to be exposed to clear motivation and careful explanation of the basics of the present-day apparatus of mathematical physics." (Ivailo Mladenov, Mathematical Reviews).

This book draws on the latest research to discuss the history and development of high-entropy alloys and ceramics in bulk, film, and fiber form. High-entropy materials have recently been developed using the entropy of mixing and entropy of configuration of materials, and have proven to exhibit unique properties superior to those of conventional materials. The field of high-entropy alloys was born in 2004, and has since been developed for both scientific and engineering applications. Although there is extensive literature, this field is rapidly transforming. This book highlights the cutting edge of high-entropy materials, including their fundamentals and applications. Above all, it reflects two major milestones in their development: the equi-atomic ratio single-phase high-entropy alloys; and the non-equi-atomic ratio dual-phase high-entropy alloys.

The concept of entropy arises in diverse branches of science, including physics, where it plays a crucial role. However, the nature of entropy as a unifying concept is not widely discussed—it is dealt with in a piecemeal manner within different contexts. The interpretation of the concept is also subtly different in each case. This book will draw these diverse threads together and present entropy as one of the crucial physical concepts. It will cover a range of different applications of entropy, from the classical theory of thermodynamics, the statistical approach, entropy in quantum theory, information theory and finally, its manifestation in black hole physics. Each will be presented in a manner suitable for undergraduates and interested laypersons with no previous knowledge. The book will take an overview of these areas and see to what extent the concept of entropy is being treated in the same way in each, and how it differs. Key Features: Provides an accessible introduction to the exciting topic of entropy, setting out its manifestations in classical thermodynamics, statistical mechanics, and information theory Covers applications in black holes, quantum theory, and Big Bang cosmology

Textbook concisely introduces engineering thermodynamics, covering concepts including energy, entropy, equilibrium and reversibility Novel explanation of entropy and the second law of thermodynamics Presents abstract ideas in an easy to understand manner Includes solved examples and end of chapter problems Accompanied by a website hosting a solutions manual

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.

This is a sequel to the author's book entitled “Entropy Demystified” (Published by World Scientific, 2007). The aim is essentially the same as that of the previous book by the author: to present Entropy and the Second Law as simple, meaningful and comprehensible concepts. In addition, this book presents a series of “experiments” which are designed to help the reader discover entropy and the Second Law. While doing the experiments, the reader will encounter three most fundamental probability distributions featuring in Physics: the Uniform, the Boltzmann and the Maxwell-Boltzmann distributions. In addition, the concepts of entropy and the Second Law will emerge naturally from these experiments without a tinge of mystery. These concepts are explained with the help of a few familiar ideas of probability and information theory.The main “value” of the book is to introduce entropy and the Second Law in simple language which renders it accessible to any reader who can read and is curious about the basic laws of nature. The book is addressed to anyone interested in science and in understanding natural phenomenon. It will afford the reader the opportunity to discover one of the most fundamental laws of physics — a law that has resisted complete understanding for over a century. The book is also designed to be enjoyable.There is no other book of its kind (except “Entropy Demystified” by the same author) that offers the reader a unique opportunity to discover one of the most profound laws — sometimes viewed as a mysterious — while comfortably playing with familiar games. There are no pre-requisites expected from the readers; all that the reader is expected to do is to follow the experiments or imagine doing the experiments and reach the inevitable conclusions.

When, in 1984?86, Richard P. Feynman gave his famous course on computation at the California Institute of Technology, he asked Tony Hey to adapt his lecture notes into a book. Although led by Feynman, the course also featured, as occasional guest speakers, some of the most brilliant men in science at that time, including Marvin Minsky, Charles Bennett, and John Hopfield. Although the lectures are now thirteen years old, most of the material is timeless and presents a ?Feynmanesque? overview of many standard and some not-so-standard topics in computer science such as reversible logic gates and quantum computers.