Elementary Principles in Statistical Mechanics: Developed with Especial Reference to the Rational Foundation of Thermodynamics

Josiah Willard Gibbs

doi:10.1017/CBO9780511686948

Elementary Principles in Statistical Mechanics

Developed with Especial Reference to the Rational Foundation of Thermodynamics

Josiah Willard Gibbs (1839–1903) was the greatest American mathematician and physicist of the nineteenth century. He played a key role in the development of vector analysis (his book on this topic is also reissued in this series), but his deepest work was in the development of thermodynamics and statistical physics. This book, Elementary Principles in Statistical Mechanics, first published in 1902, gives his mature vision of these subjects. Mathematicians, physicists and engineers familiar with such things as Gibbs entropy, Gibbs inequality and the Gibbs distribution will find them here discussed in Gibbs' own words.

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Elementary Principles in Statistical Mechanics

Developed with Especial Reference to the Rational Foundation of Thermodynamics

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Contents

Frontmatter
pp i-vi

PREFACE
pp vii-xii

Contents
pp xiii-xviii

ELEMENTARY PRINCIPLES IN STATISTICAL MECHANICS
pp 1-2

CHAPTER I - GENERAL NOTIONS. THE PRINCIPLE OF CONSERVATION OF EXTENSION-IN-PHASE
pp 3-19

CHAPTER II - APPLICATION OF THE PRINCIPLE OF CONSERVATION OF EXTENSION-IN-PHASE TO THE THEORY OF ERRORS
pp 20-25

CHAPTER III - APPLICATION OF THE PRINCIPLE OF CONSERVATION OF EXTENSION-IN-PHASE TO THE INTEGRATION OF THE DIFFERENTIAL EQUATIONS OF MOTION
pp 26-31

CHAPTER IV - ON THE DISTRIBUTION-IN-PHASE CALLED CANONICAL, IN WHICH THE INDEX OF PROBABILITY IS A LINEAR FUNCTION OF THE ENERGY
pp 32-45

CHAPTER V - AVERAGE VALUES IN A CANONICAL ENSEMBLE OF SYSTEMS
pp 46-56

CHAPTER VI - EXTENSION-IN-CONFIGURATION AND EXTENSION-IN-VELOCITY
pp 57-67

CHAPTER VII - FARTHER DISCUSSION OF AVERAGES IN A CANONICAL ENSEMBLE OF SYSTEMS
pp 68-86

CHAPTER VIII - ON CERTAIN IMPORTANT FUNCTIONS OF THE ENERGIES OF A SYSTEM
pp 87-99

CHAPTER IX - THE FUNCTION ϕ AND THE CANONICAL DISTRIBUTION
pp 100-114

CHAPTER X - ON A DISTRIBUTION IN PHASE CALLED MICROCANONICAL IN WHICH ALL THE SYSTEMS HAVE THE SAME ENERGY
pp 115-128

CHAPTER XI - MAXIMUM AND MINIMUM PROPERTIES OF VARIOUS DISTRIBUTIONS IN PHASE
pp 129-138

CHAPTER XII - ON THE MOTION OF SYSTEMS AND ENSEMBLES OF SYSTEMS THROUGH LONG PERIODS OF TIME
pp 139-151

CHAPTER XIII - EFFECT OF VARIOUS PROCESSES ON AN ENSEMBLE OF SYSTEMS
pp 152-164

CHAPTER XIV - DISCUSSION OF THERMODYNAMIC ANALOGIES
pp 165-186

CHAPTER XV - SYSTEMS COMPOSED OF MOLECULES
pp 187-207

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Elementary Principles in Statistical Mechanics

Developed with Especial Reference to the Rational Foundation of Thermodynamics

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