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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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