Elementary Principles in Statistical Mechanics: Developed with Especial Reference to the Rational Foundation of ThermodynamicsCambridge University Press, 1960 - Počet stran: 207 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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GENERAL NOTIONS THE PRINCIPLE OF CONSERVATION | 3 |
Principle of conservation of densityinphase | 9 |
Coefficient and index of probability of phase | 16 |
Application of the principle of conservation of probability of phase | 23 |
ON THE DISTRIBUTIONINPHASE CALLED CANONICAL | 32 |
Case in which the forces are linear functions of the displacements | 41 |
Average value of total kinetic energy for any given configuration | 49 |
Second proof of the same proposition | 55 |
Average values of powers of the anomalies of the energies | 83 |
Geometrical illustration | 99 |
ON A DISTRIBUTION IN PHASE CALLED MICROCANONI | 115 |
CHAPTER XI | 129 |
ON THE MOTION OF SYSTEMS AND ENSEMBLES OF SYS | 139 |
CHAPTER XIII | 152 |
If a system of a great number of degrees of freedom is microcanon | 183 |
Equilibrium with respect to gain or loss of molecules | 189 |
CHAPTER VII | 68 |
Average values of powers of the energies | 75 |
Average value of number of any kind of molecules | 198 |
When the number of particles in a system is to be treated | 206 |
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A₁ A₂ average value canonical distribution canonical ensemble Chapter coefficient of probability condition conservation of extension-in-phase considered constants of motion coördinates and momenta corresponding da₁ da₂ degrees of freedom denote density density-in-phase determined distributed in phase dp₁ dq₁ dqı ensemble of systems entropy Ep Ep evidently expressed extension-in-configuration extension-in-velocity external coördinates forces formula give given limits identical independent index of probability infinite infinitesimal integral equations kinetic energy linear functions microcanonical ensemble modulus multiple integral number of degrees number of systems p's and q's P₁ partial energies particles potential energy principle of conservation probability of phase probability-coefficient q₁ quadratic function quantities r₁ regarded relating represented respect statistical equilibrium suffixes suppose system of coördinates temperature theorem thermodynamics tion V₁ V₂ vanishes variables velocities whole ensemble zero αφ аф