Introduction to Entropy

Jonathan Allday taught physics at a range of schools in the UK. After attending the Liverpool Blue Coat School, he took his first degree in Natural Sciences at Cambridge, then gained a PhD in particle physics in 1989 at Liverpool University. Shortly after this, he started work on Quarks Leptons and the Big Bang, now published by Taylor & Francis and available in its third edition, which was intended as a rigorous but accessible introduction to these topics. Since then, he has also written Apollo in Perspective, Quantum Reality (now in its second edition), and Space-time, co-authored a successful textbook and contributed to an encyclopaedia for young scientists. He has also written on aspects of the history and philosophy of science. Outside of physics, Jonathan has a keen interest in cricket and Formula 1.Simon Hands was also educated at the Blue Coat School and Cambridge University, followed by a PhD in theoretical particle physics at the University of Edinburgh. After research positions at the universities of Oxford, Illinois, Glasgow, and then CERN, he taught and researched theoretical and computational physics at Swansea University for almost 30 years. He moved to the University of Liverpool in 2021, where he helps manage the DiRAC high-performance computing facility for astronomy, nuclear and particle physics theory. An elected Fellow of the Learned Society of Wales, Simon enjoys singing and cycling.

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 19th 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 LondonThis 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

• Introduction: What is Entropy? Chapter 1: Zero. Chapter 2: One. Chapter 3: Ideal. Chapter 4: Two. Chapter 5: Omega. Chapter 6: The Quantum Realm. Chapter 7: Ensembles, Energy Levels and Microstates. Chapter 8: Identical Particles. Chapter 9: The Grand Canonical Ensemble. Chapter 10: Entropy and the Time Evolution of Quantum States. Chapter 11: The Density Matrix. Chapter 12: Quantum Entropy. Chapter 13: Life. Chapter 14: Information. Chapter 15: Death. Chapter 16: Black. Chapter 17: Afterthoughts. Appendix MA: Mathematical Preliminaries. PA1: Physics Appendix. Bibliography. Index.