The Conceptual Foundations of the Statistical Approach in Mechanics
In this concise classic, Paul Ehrenfest ― one of the twentieth century's greatest physicists ― reformulated the foundations of the statistical approach in mechanics. Originally published in 1912, this classic has lost little of its scientific and didactic value, and is suitable for advanced undergraduate and graduate students of physics and historians of science.
Part One describes the older formulation of statistico-mechanical investigations (kineto-statistics of the molecule). Part Two takes up the modern formulation of kineto-statistics of the gas model, and Part Three explores W. B. Gibbs's major work, Elementary Principles in Statistical Mechanics and its coverage of such topics as the problem of axiomatization in kineto-statistics, the introduction of canonical and microcanonical distributions, and the analogy to the observable behavior of thermodynamic systems. The book concludes with the authors' original notes, a series of useful appendixes, and a helpful bibliography.
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analogies Appendix to Section arbitrary assume assumption atoms average values Boltz Boltzmann calculation canonical distribution canonical ensemble Chap Clausius constant corresponding curve defined degrees of freedom derivation deviations discussion distributed ensembles distribution Eq Ehrenfest Einstein energy surface ensemble of gas ensembles of systems entropy equations ergodic hypothesis ergodic system formulation G-points gas model gas quantum Gastheorie Gibbs Gibbs’s given group of motions H-curves H-function H-theorem H. A. Lorentz hypothesis of molecular image points infinitely interval investigations irreversible processes Jeans kinetic energy kinetic theory large number Let us consider Let us denote Maxwell distribution Maxwell-Boltzmann distribution measure microcanonical molecular chaos molecules nonstationary p-distribution P-molecules parameters r1 phase point Phys Planck postulates probability problem quantity region relative frequency remarks Smoluchowski Statistical Mechanics statistico-mechanical Stosszahlansatz temperature theorem theory of gases thermal equilibrium thermodynamics tion total energy u-space Umkehreinwand velocity distribution Wiederkehreinwand Zeitschr Zermelo