A Student's Guide to Entropy

Citation

Lemons, D. S. (2013). A Student's Guide to Entropy. Cambridge University Press.

Chapter Summary

The book has a preface, eight chapters, a short epilogue titled "What is entropy?" and six appendices (physical constants and standard definitions, a formulary, a glossary, a time line, answers to problems, and annotated further reading). The paperback is listed at 200 pages. The publisher says it contains over 20 worked examples and around 50 end-of-chapter exercises.

Chapter 1: Thermodynamic entropy

The chapter opens with thermodynamics as the science of macroscopic objects described by a handful of variables such as pressure, volume, temperature and energy. It states that entropy follows from the first and second laws and that its main role in thermodynamics is to quantify the irreversibility of a process, telling which processes of an isolated system are possible and which are not. It is the longest chapter (pages 1 to 31).

Chapter 2: Statistical entropy

The second chapter looks inside the thermodynamic "black box" through Boltzmann and atoms. The publisher singles out the construction of statistical entropy from desired properties as an innovative feature of the book.

Chapter 3: Entropy of classical systems

The entropy of classical systems is derived, according to the publisher's description, from purely classical assumptions.

Chapter 4: Entropy of quantized systems

The title marks the move from classical to quantized systems; the chapter-opening preview was not available, so no more is claimed here.

Chapter 5: Entropy of a non-isolated system

The shortest chapter (pages 96 to 104); its title indicates that entropy is now considered for a system that is not isolated.

Chapters 6–7: Entropy of fermion systems; Entropy of systems of bosons

These chapters give the statistical thermodynamics approach to the ideal Fermi and ideal Bose gases that the publisher lists among the book's innovations. The publisher's preview of the fermion chapter begins with symmetries and wave functions: a system wave function may be symmetric or antisymmetric under exchange of identical particles, which leads to two ways of counting microstates.

Chapter 8: Entropy of information

The last chapter turns to messages and message sources, the setting of information theory, and connects the entropy of physics and chemistry with the measure of uncertainty that Shannon investigated.

Epilogue: What is entropy?

The epilogue gathers figurative descriptions of entropy considered in the book: transformation content, disorder, uncertainty, spread in phase space and missing information. It also notes that disorder has fallen out of favour as a description.

Key Concepts

Chapters 1–3: From heat to microstates

• Irreversibility: the property of a process that entropy quantifies in thermodynamics.
• Thermodynamic variables and equations of state: the macroscopic description on which the first chapter relies.
• Statistical entropy: the entropy defined from the counting of microscopic states.

Chapters 4–7: Quantum statistics

• Multiplicity of a quantized system: the number of accessible microstates, which the preview of the fermion chapter links to the symmetry of the wave function.
• Fermions and bosons: particles with antisymmetric or symmetric wave functions, giving the ideal Fermi and Bose gases.

Chapter 8 and Epilogue

• Information entropy: Shannon's measure of uncertainty and its parallel with physical entropy.
• Figurative descriptions of entropy: the five listed in the epilogue.

Critical Analysis

Strengths

• Focused scope. The book concentrates on a single concept and follows it from thermodynamics through statistical mechanics to information theory, in about 160 pages of chapters.
• Step-by-step derivations with worked examples. The publisher stresses that derivations are worked through step by step, with over 20 worked examples and around 50 exercises.
• Support material. The glossary defines all essential terms, the time line shows important developments, and an annotated list of further reading is included; answers to the problems are in the back.
• Reviews. Effrosyni Seitaridou, in the American Journal of Physics, described the explanations as thorough, clear and succinct. Choice called it well written and highly recommended. Prashant Khare, in Contemporary Physics, praised the methodical derivations and the plain-language explanation of their physical meaning, and a reviewer in The Observatory recommended it as a main, inexpensive text for a statistical mechanics course.

Limitations

• Not a complete course. It treats entropy, not the whole of thermodynamics or statistical mechanics, and the contents show no chapters on topics such as phase transitions or interacting systems; the book is presented as a supplement to undergraduate courses.
• Quantum material needs preparation. The fermion and boson chapters rely on wave-function symmetry, so a first quantum mechanics course helps even though the frontmatter lists only calculus and introductory heat as prerequisites.

Where It Fits in the Course

Lemons is a short companion rather than a main text. Schroeder's An Introduction to Thermal Physics treats thermodynamics and statistical mechanics together, defining temperature and entropy by counting microstates, and is the natural main book; Blundell and Blundell's Concepts in Thermal Physics covers a similar range in many short chapters and includes information among its applications. Rex's revision of Finn's Thermal Physics is a concise classical thermodynamics text with added statistical mechanics, and Baierlein's Thermal Physics connects macroscopic laws with microscopic probability. Pathria and Beale's Statistical Mechanics is the graduate treatment to move to for ensemble theory and interacting systems. Lemons suits a reader who wants entropy explained on its own, before, during or after one of these courses.

How to Use This Book

The book suits undergraduates in physics, engineering, chemistry or mathematics who have met heat and temperature and know introductory calculus.

A practical plan: read the preface and Chapters 1 and 2 first, which fix the thermodynamic and statistical definitions. Chapter 3 follows naturally; Chapters 4 to 7 matter for readers who will meet Fermi and Bose gases, and can be postponed otherwise. Chapter 8 can be read independently by those interested in information theory, and the epilogue is a good summary at the end. Work the exercises and check them against the answers, and use the glossary and time line as reference.