Introduction to Entropy

The Way of the World

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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 draws these diverse threads together and present entropy as one of the crucial physical concepts. It covers a range of different applications of entropy, from the classical theory of thermodynamics, the statistical approach, entropy in quantum theory, informatio...

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Undergraduates seem to arrive at university fascinated by quantum mechanics and relativity; by Schrödinger's Cat and black holes. And indeed every physics degree programme will develop this interest. But these are just two pillars of physics, to which can be added a third, a central pillar that concerns the behaviour of physical objects, be they atoms or stars, in circumstances where they collectively demonstrate 'irreversible' behaviour. A major consequence of this is the 'arrow of time', where stuff happens that has a beginning, a middle and an end, and it turns out that the property that characterises this narrative is entropy production.

Jonathan Allday and Simon Hands have written a book that aims to raise the profile of

entropy, and the wider topics of thermodynamics and statistical mechanics, to levels of interest enjoyed by the better known major themes of physics. To this end they note that encountering thermodynamics 'has been a source of dismay to generations of students who naively imagined they'd chosen physics to study quarks, lasers and the Big Bang.... Our advice: stay patient'.

The book is wide-ranging and engaging, and is intended for a readership of 'undergraduates and interested laypersons', to which might be added keen pre-university students, an audience served by some of Allday's previous books.

The book falls into three parts, two of which would be readily accessible to interested laypersons. The first part follows a traditional path through classical and statistical thermodynamics, laying foundations for an understanding of the concept of entropy and the special character of the second law of thermodynamics.

The middle part suits a better prepared readership, since it introduces aspects of quantum mechanics using mathematics that is quite advanced, though commendably transparent in that derivations are presented in detail. The material would provide illumination for an advanced undergraduate statistical mechanics module, especially in its handling of the density matrix.

The third part returns to a gentler discussion of the implications of the second law: to life, the universe and other matters. The fundamental connection between thermodynamic entropy and information science is developed. This is a fine coda to a book that takes its reader from early 19^th century ideas concerning the efficiency of steam engines to the modern (less practical!) study of information processing in black holes.

In summary, 'Introduction to Entropy: the Way of the World' makes a compelling case that describing the irreversibility of processes in the physical world is fundamental science: a pillar of physics to be promoted!

- Ian Ford, Professor of Physics, University College London

This is an interesting and engaging book to anyone with an undergraduate education in physics, or above, who wants to understand the concept of entropy in all its manifestations in modern physics. It covers a great deal of territory but the narrative is coherent and well thought-out the material is very well organized and presented.

- Peter Coles, Professor of Theoretical Physics, Maynooth University, December 2024

'I was delighted to see that Allday and Hands have provided us with new ways of enjoying thermodynamics with their book "Introduction to Entropy: The Way of the World". Thermodynamics is not always ascribed the same glamour as other areas of theoretical physics, but anyone who takes the time to read this book will be convinced that this is a big oversight, and that the concept of entropy is a key philosophical importance to our notions of both time and information.'

- Sarah Harris, Professor of Biological Physics, University of Sheffield, January 2025

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