Article ID: CBB559121662

The Development of Ensemble Theory (2015)

unapi

This paper investigates the history of statistical mechanics from the viewpoint of the development of the ensemble theory from 1871 to 1902. In 1871, Ludwig Boltzmann introduced a prototype model of an ensemble that represents a polyatomic gas. In 1879, James Clerk Maxwell defined an ensemble as copies of systems of the same energy. Inspired by H.W. Watson, he called his approach “statistical”. Boltzmann and Maxwell regarded the ensemble theory as a much more general approach than the kinetic theory. In the 1880s, influenced by Hermann von Helmholtz, Boltzmann made use of ensembles to establish thermodynamic relations. In Elementary Principles in Statistical Mechanics of 1902, Josiah Willard Gibbs tried to get his ensemble theory to mirror thermodynamics, including thermodynamic operations in its scope. Thermodynamics played the role of a “blind guide”. His theory of ensembles can be characterized as more mathematically oriented than Einstein’s theory proposed in the same year. Mechanical, empirical, and statistical approaches to foundations of statistical mechanics are presented. Although it was formulated in classical terms, the ensemble theory provided an infrastructure still valuable in quantum statistics because of its generality.

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Authors & Contributors
Badino, Massimiliano
Peliti, Luca
Uffink, Jos
Stachel, John J.
Shenker, Orly R.
Rowlinson, John S.
Journals
Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
Physics in Perspective
Studia Historiae Scientiarum
Physis: Rivista Internazionale di Storia della Scienza
Notes and Records: The Royal Society Journal of the History of Science
Metascience: An International Review Journal for the History, Philosophy and Social Studies of Science
Publishers
Pavia University Press
Oxford University Press
Birkhäuser
Cambridge University Press
Concepts
Statistical mechanics
Physics
Thermodynamics
Quantum mechanics
Biographies
Probability and statistics
People
Boltzmann, Ludwig
Einstein, Albert
Maxwell, James Clerk
Poincaré, Jules Henri
Helmholtz, Hermann Ludwig Ferdinand von
Ehrenfest, Paul
Time Periods
20th century, early
19th century
20th century
21st century
20th century, late
Places
United States
Germany
France
Austria
Soviet Union
Vienna (Austria)
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