Article ID: CBB559121662

The Development of Ensemble Theory (2015)


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.

Citation URI

Similar Citations

Article Brown, Harvey R.; Myrvold, Wayne; Uffink, Jos; (2009)
Boltzmann's H-Theorem, Its Discontents, and the Birth of Statistical Mechanics (/isis/citation/CBB000933693/)

Article Rowlinson, J. S.; (2005)
Einstein: The Classical Physicist (/isis/citation/CBB000651781/)

Chapter Luca Peliti; Raúl Rechtman; (2017)
Einstein’s approach to Statistical Mechanics (/isis/citation/CBB012214251/)

Article Daniela Monaldi; (2019)
The Statistical Style of Reasoning and the Invention of Bose-Einstein Statistics (/isis/citation/CBB327349848/)

Article Navarro, Luis; Pérez, Enric; (2006)
Paul Ehrenfest: The Genesis of the Adiabatic Hypothesis, 1911--1914 (/isis/citation/CBB000670059/)

Article Badino, Massimiliano; Friedrich, Bretislav; (2013)
Much Polyphony but Little Harmony: Otto Sackur's Groping for a Quantum Theory of Gases (/isis/citation/CBB001320410/)

Article Pechenkin, Alexander; (2012)
The Early Statistical Interpretations of Quantum Mechanics in the USA and USSR (/isis/citation/CBB001210779/)

Article Guzmán, Ricardo; Cervera, José Antonio; (2006)
La mecánica estadística: sus orígenes y sus paradojas a la luz de los escritos de Paul y Tatiana Ehrenfest (/isis/citation/CBB000930275/)

Article Lavis, D. A.; (2005)
Boltzmann and Gibbs: An Attempted Reconciliation (/isis/citation/CBB000771639/)

Book Hemmo, Meir; Shenker, Orly R.; (2012)
The Road to Maxwell's Demon, Conceptual Foundations of Statistical Mechanics (/isis/citation/CBB001500356/)

Article Reiter, Wolfgang L.; (2007)
In Memoriam Ludwig Boltzmann: A Life of Passion (/isis/citation/CBB000850200/)

Article Boughn, Stephen; Reginatto, Marcel; (2013)
A Pedestrian Approach to the Measurement Problem in Quantum Mechanics (/isis/citation/CBB001320783/)

Article D'Abramo, Germano; (2012)
The Peculiar Status of the Second Law of Thermodynamics and the Quest for Its Violation (/isis/citation/CBB001211050/)

Article Badino, Massimiliano; (2005)
Il contributo di Khinchin al problema ergodico (/isis/citation/CBB000701089/)

Article Campisi, Michele; (2005)
On the Mechanical Foundations of Thermodynamics: The Generalized Helmholtz Theorem (/isis/citation/CBB000771640/)

Essay Review Hagar, Amit; (2014)
Demons in Physics (/isis/citation/CBB001500355/)

Book Howard, Don; Stachel, John; (2000)
Einstein: The formative years, 1879-1909 (/isis/citation/CBB000110592/)

Authors & Contributors
Badino, Massimiliano
Peliti, Luca
Uffink, Jos
Stachel, John J.
Shenker, Orly R.
Rowlinson, John S.
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
Pavia University Press
Oxford University Press
Cambridge University Press
Statistical mechanics
Quantum mechanics
Probability and statistics
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
United States
Soviet Union
Vienna (Austria)

Be the first to comment!

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}

Log in or register to comment