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Book contents
- Frontmatter
- PREFACE
- Contents
- ELEMENTARY PRINCIPLES IN STATISTICAL MECHANICS
- CHAPTER I GENERAL NOTIONS. THE PRINCIPLE OF CONSERVATION OF EXTENSION-IN-PHASE
- CHAPTER II APPLICATION OF THE PRINCIPLE OF CONSERVATION OF EXTENSION-IN-PHASE TO THE THEORY OF ERRORS
- CHAPTER III APPLICATION OF THE PRINCIPLE OF CONSERVATION OF EXTENSION-IN-PHASE TO THE INTEGRATION OF THE DIFFERENTIAL EQUATIONS OF MOTION
- CHAPTER IV ON THE DISTRIBUTION-IN-PHASE CALLED CANONICAL, IN WHICH THE INDEX OF PROBABILITY IS A LINEAR FUNCTION OF THE ENERGY
- CHAPTER V AVERAGE VALUES IN A CANONICAL ENSEMBLE OF SYSTEMS
- CHAPTER VI EXTENSION-IN-CONFIGURATION AND EXTENSION-IN-VELOCITY
- CHAPTER VII FARTHER DISCUSSION OF AVERAGES IN A CANONICAL ENSEMBLE OF SYSTEMS
- CHAPTER VIII ON CERTAIN IMPORTANT FUNCTIONS OF THE ENERGIES OF A SYSTEM
- CHAPTER IX THE FUNCTION ϕ AND THE CANONICAL DISTRIBUTION
- CHAPTER X ON A DISTRIBUTION IN PHASE CALLED MICROCANONICAL IN WHICH ALL THE SYSTEMS HAVE THE SAME ENERGY
- CHAPTER XI MAXIMUM AND MINIMUM PROPERTIES OF VARIOUS DISTRIBUTIONS IN PHASE
- CHAPTER XII ON THE MOTION OF SYSTEMS AND ENSEMBLES OF SYSTEMS THROUGH LONG PERIODS OF TIME
- CHAPTER XIII EFFECT OF VARIOUS PROCESSES ON AN ENSEMBLE OF SYSTEMS
- CHAPTER XIV DISCUSSION OF THERMODYNAMIC ANALOGIES
CHAPTER XV - SYSTEMS COMPOSED OF MOLECULES
Published online by Cambridge University Press: 05 August 2011
- Frontmatter
- PREFACE
- Contents
- ELEMENTARY PRINCIPLES IN STATISTICAL MECHANICS
- CHAPTER I GENERAL NOTIONS. THE PRINCIPLE OF CONSERVATION OF EXTENSION-IN-PHASE
- CHAPTER II APPLICATION OF THE PRINCIPLE OF CONSERVATION OF EXTENSION-IN-PHASE TO THE THEORY OF ERRORS
- CHAPTER III APPLICATION OF THE PRINCIPLE OF CONSERVATION OF EXTENSION-IN-PHASE TO THE INTEGRATION OF THE DIFFERENTIAL EQUATIONS OF MOTION
- CHAPTER IV ON THE DISTRIBUTION-IN-PHASE CALLED CANONICAL, IN WHICH THE INDEX OF PROBABILITY IS A LINEAR FUNCTION OF THE ENERGY
- CHAPTER V AVERAGE VALUES IN A CANONICAL ENSEMBLE OF SYSTEMS
- CHAPTER VI EXTENSION-IN-CONFIGURATION AND EXTENSION-IN-VELOCITY
- CHAPTER VII FARTHER DISCUSSION OF AVERAGES IN A CANONICAL ENSEMBLE OF SYSTEMS
- CHAPTER VIII ON CERTAIN IMPORTANT FUNCTIONS OF THE ENERGIES OF A SYSTEM
- CHAPTER IX THE FUNCTION ϕ AND THE CANONICAL DISTRIBUTION
- CHAPTER X ON A DISTRIBUTION IN PHASE CALLED MICROCANONICAL IN WHICH ALL THE SYSTEMS HAVE THE SAME ENERGY
- CHAPTER XI MAXIMUM AND MINIMUM PROPERTIES OF VARIOUS DISTRIBUTIONS IN PHASE
- CHAPTER XII ON THE MOTION OF SYSTEMS AND ENSEMBLES OF SYSTEMS THROUGH LONG PERIODS OF TIME
- CHAPTER XIII EFFECT OF VARIOUS PROCESSES ON AN ENSEMBLE OF SYSTEMS
- CHAPTER XIV DISCUSSION OF THERMODYNAMIC ANALOGIES
Summary
The nature of material bodies is such that especial interest attaches to the dynamics of systems composed of a great number of entirely similar particles, or, it may be, of a great number of particles of several kinds, all of each kind being entirely similar to each other. We shall therefore proceed to consider systems composed of such particles, whether in great numbers or otherwise, and especially to consider the statistical equilibrium of ensembles of such systems. One of the variations to be considered in regard to such systems is a variation in the numbers of the particles of the various kinds which it contains, and the question of statistical equilibrium between two ensembles of such systems relates in part to the tendencies of the various kinds of particles to pass from the one to the other.
First of all, we must define precisely what is meant by statistical equilibrium of such an ensemble of systems. The essence of statistical equilibrium is the permanence of the number of systems which fall within any given limits with respect to phase. We have therefore to define how the term “phase” is to be understood in such cases. If two phases differ only in that certain entirely similar particles have changed places with one another, are they to be regarded as identical or different phases? If the particles are regarded as indistinguishable, it seems in accordance with the spirit of the statistical method to regard the phases as identical.
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- Elementary Principles in Statistical MechanicsDeveloped with Especial Reference to the Rational Foundation of Thermodynamics, pp. 187 - 207Publisher: Cambridge University PressPrint publication year: 2010First published in: 1902