Anxiety and the Equation: Understanding Boltzmann's Entropy

by Eric Johnson

Overview

A man and his equation: the anxiety-plagued nineteenth-century physicist who contributed significantly to our understanding of the second law of thermodynamics.

Ludwig Boltzmann's grave in Vienna's Central Cemetery bears a cryptic epitaph: S = k log W. This equation was Boltzmann's great discovery, and it contributed significantly to our understanding of the second law of thermodynamics. In Anxiety and the Equation, Eric Johnson tells the story of a man and his equation: the anxiety-plagued nineteenth-century physicist who did his most important work as he struggled with mental illness.

Johnson explains that “S” in Boltzmann's equation refers to entropy, and that entropy is the central quantity in the second law of thermodynamics. The second law is always on, running in the background of our lives, providing a way to differentiate between past and future. We know that the future will be a state of higher entropy than the past, and we have Boltzmann to thank for discovering the equation that underlies that fundamental trend. Johnson, accessibly and engagingly, reassembles Boltzmann's equation from its various components and presents episodes from Boltzmann's life—beginning at the end, with “Boltzmann Kills Himself” and “Boltzmann Is Buried (Not Once, But Twice).” Johnson explains the second law in simple terms, introduces key concepts through thought experiments, and explores Boltzmann's work. He argues that Boltzmann, diagnosed by his contemporaries as neurasthenic, suffered from an anxiety disorder. He was, says Johnson, a man of reason who suffered from irrational concerns about his work, worrying especially about opposition from the scientific establishment of the day.

Johnson's clear and concise explanations will acquaint the nonspecialist reader with such seemingly esoteric concepts as microstates, macrostates, fluctuations, the distribution of energy, log functions, and equilibrium. He describes Boltzmann's relationships with other scientists, including Max Planck and Henri Poincaré, and, finally, imagines “an alternative ending,” in which Boltzmann lived on and died of natural causes.

Product Details

ISBN-13:	9780262348546
Publisher:	MIT Press
Publication date:	10/23/2018
Series:	The MIT Press
Sold by:	Penguin Random House Publisher Services
Format:	eBook
Pages:	192
File size:	3 MB
Age Range:	18 Years

About the Author

Eric Johnson is Associate Professor in the Department of Chemistry at Mount St. Joseph University in Cincinnati.

Table of Contents

Acknowledgments ix

Introduction xi

1 Boltzmann Kills Himself 1

2 Boltzmann Is Buried (Not Once, But Twice) 3

3 Start Simple 7

4 Before Things Got Weird 11

5 Postmortem Psychiatry 13

6 But How Crazy? 19

7 Not Quite Big Numbers 27

8 Big Enough Numbers 33

9 And Everything In Between 39

10 A Case for Anxiety 47

11 One of the Many Benefits of Modernity 51

12 And Yet It Moves 55

13 Follow the Leader 63

14 The Night Before 71

15 The Next Day 73

16 One's Harshest Critic 77

17 Something Like a Mathematical Supplement 83

18 You May Now Return to Your Seats 87

19 Boltzmann's Constant 93

20 Human Factors 105

21 In Search of a Better Analogy 121

22 Equilibrium You Can Count On 133

23 A Rigorous Examination of the Obvious 147

24 The Farewell Tour 159

25 An Alternative Ending 169

Notes 171

Index 177

What People are Saying About This

Endorsement

“Johnson has written a gripping, droll, and lucid account of the microscopic understanding of entropy, interwoven with the poignant story of Boltzmann. The ideas in this widely accessible book are among the most important in the scientific view of our manifold universe.”

—Kannan Jagannathan, Professor of Physics, Amherst College

From the Publisher

“A clear, lively, and accurate account of Ludwig Boltzmann's life and work and the meaning of his most famous contribution to science: the equation that describes the entropy of an isolated system.”

—Don S. Lemons, Professor of Physics Emeritus, Bethel College, author of  A Student's Guide to Entropy, Thermodynamic Weirdness: From Fahrenheit to Clausius, and Drawing Physics: 2600 Years of Discovery from Thales to Higgs

“Boltzmann emerges as a brilliant but troubled mind whose groundbreaking ideas and sympathetic afflictions feel more at home in the twenty-first century than the nineteenth. In Johnson's capable hands, Boltzmann's professional and personal story becomes one for the ages.”

—Ethan Siegel, Theoretical Astrophysicist, author of Beyond the Galaxy and Treknology

“Johnson has written a gripping, droll, and lucid account of the microscopic understanding of entropy, interwoven with the poignant story of Boltzmann.  The ideas in this widely accessible book are among the most important in the scientific view of our manifold universe.”

—Kannan Jagannathan, Professor of Physics, Amherst College

Editorial Reviews

Johnson's discussion of Boltzmann's equation (which is credited to him because he came up with the key concepts, though he never explicitly wrote it in the modern form) is anchored in extremely concrete discussions of random processes involving small numbers of particles, and calculating the likelihood of each of the “microstates” of these systems. Thanks to these examples of particles hopping between positions and energy states, he is able to put together one of the clearest explanations I've seen of what entropy is in a statistical sense, and how it functions. He even explains why it makes sense for a logarithm to appear, which I had never seen before.—Chad Orzel, Forbes—

Johnson writes pedagogically, but not pedantically. He is charming and colloquial. He uses (maybe a few too many) parenthetical asides. The book barely tops 150 pages, with short chapters switching easily between history and science; it's a book that can be read lightly and in a weekend.

—DigBoston—

a piece of scientific popularization as well as a remarkably humane book.

—Inside Higher Ed—

From the Publisher