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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 XIII - EFFECT OF VARIOUS PROCESSES ON AN ENSEMBLE OF SYSTEMS
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
In the last chapter and in Chapter I we have considered the changes which take place in the course of time in an ensemble of isolated systems. Let us now proceed to consider the changes which will take place in an ensemble of systems under external influences. These external influences will be of two kinds, the variation of the coordinates which we have called external, and the action of other ensembles of systems. The essential difference of the two kinds of influence consists in this, that the bodies to which the external coordinates relate are not distributed in phase, while in the case of interaction of the systems of two ensembles, we have to regard the fact that both are distributed in phase. To find the effect produced on the ensemble with which we are principally concerned, we have therefore to consider single values of what we have called external coördinates, but an infinity of values of the internal coördinates of any other ensemble with which there is interaction.
Or, — to regard the subject from another point of view, — the action between an unspecified system of an ensemble and the bodies represented by the external coördinates, is the action between a system imperfectly determined with respect to phase and one which is perfectly determined; while the interaction between two unspecified systems belonging to different ensembles is the action between two systems both of which are imperfectly determined with respect to phase.
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- Elementary Principles in Statistical MechanicsDeveloped with Especial Reference to the Rational Foundation of Thermodynamics, pp. 152 - 164Publisher: Cambridge University PressPrint publication year: 2010First published in: 1902