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Basic principles

Barry M. McCoy

in Advanced Statistical Mechanics

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199556632
eISBN:
9780191723278
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199556632.003.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter reviews the basic results of thermodynamics. It derives the basic formulas of the canonical and grand canonical ensemble from the microcanonical ensemble. It defines the concept of a ... More


Equilibrium Statistical Mechanics

Hans-Peter Eckle

in Models of Quantum Matter: A First Course on Integrability and the Bethe Ansatz

Published in print:
2019
Published Online:
September 2019
ISBN:
9780199678839
eISBN:
9780191878589
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199678839.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

Chapter 4 reviews the basic notions of equilibrium statistical mechanics and begins with its fundamental postulate and outlines the structure of the theory using the most important of the various ... More


The Probabilistic Turn (1876–1884)

Olivier Darrigol

in Atoms, Mechanics, and Probability: Ludwig Boltzmann's Statistico-Mechanical Writings - An Exegesis

Published in print:
2018
Published Online:
March 2018
ISBN:
9780198816171
eISBN:
9780191853661
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198816171.003.0005
Subject:
Physics, Atomic, Laser, and Optical Physics, History of Physics

This chapter deals with writings in which Boltzmann expressed the statistical nature of the entropy law and temporarily made the relation between entropy and combinatorial probability a basic ... More


Ensembles in Classical Statistical Mechanics

Robert H. Swendsen

in An Introduction to Statistical Mechanics and Thermodynamics

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199646944
eISBN:
9780191775123
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199646944.003.0019
Subject:
Physics, Condensed Matter Physics / Materials

This chapter resumes the discussion of classical statistical mechanics that was begun in Part 1 of the book. Numerical methods (molecular dynamics and Monte Carlo computer simulations) of calculating ... More


Quantum Mechanical Ensemble Averages and Statistical Thermodynamics

Norman J. Morgenstern Horing

in Quantum Statistical Field Theory: An Introduction to Schwinger's Variational Method with Green's Function Nanoapplications, Graphene and Superconductivity

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198791942
eISBN:
9780191834165
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198791942.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 6 introduces quantum-mechanical ensemble theory by proving the asymptotic equivalence of the quantum-mechanical, microcanonical ensemble average with the quantum grand canonical ensemble ... More


Ensembles with hard constraints

A.C.C. Coolen, A. Annibale, and E.S. Roberts

in Generating Random Networks and Graphs

Published in print:
2017
Published Online:
May 2017
ISBN:
9780198709893
eISBN:
9780191780172
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198709893.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter introduces random graph ensembles involving hard constraints such as setting a fixed total number of links or fixed degree sequence, including properties of the partition function. It ... More


Lectures on Gas Theory (1896, 1898)

Olivier Darrigol

in Atoms, Mechanics, and Probability: Ludwig Boltzmann's Statistico-Mechanical Writings - An Exegesis

Published in print:
2018
Published Online:
March 2018
ISBN:
9780198816171
eISBN:
9780191853661
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198816171.003.0009
Subject:
Physics, Atomic, Laser, and Optical Physics, History of Physics

This chapter is devoted mostly to the two volumes of Boltzmann’s Lectures on gas theory, published in 1896 and 1898, with special attention to the novel elements in Boltzmann’s representation of his ... More


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