## Kelvin and Statistical Mechanics

*Oliver Penrose*

### in Kelvin: Life, Labours and Legacy

- Published in print:
- 2008
- Published Online:
- May 2008
- ISBN:
- 9780199231256
- eISBN:
- 9780191710803
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199231256.003.0015
- Subject:
- Mathematics, History of Mathematics

Kelvin played a big part in the development of statistical mechanics, both for equilibrium and non-equilibrium. This chapter reviews these developments, taking a particular interest in Kelvin's own ... More

## Validity and Non-Validity of Propagation of Chaos

*Karsten Matthies and Florian Theil*

### in Analysis and Stochastics of Growth Processes and Interface Models

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199239252
- eISBN:
- 9780191716911
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199239252.003.0005
- Subject:
- Mathematics, Probability / Statistics, Analysis

In this chapter a novel, rigorous approach to analyse the validity of continuum approximations for deterministic interacting particle systems is discussed. The focus is on the Boltzmann–Grad limit of ... More

## Time irreversibility and the H-theorem

*CARLO CERCIGNANI*

### in Ludwig Boltzmann: The Man Who Trusted Atoms

- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780198570646
- eISBN:
- 9780191717949
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570646.003.0005
- Subject:
- Physics, History of Physics

Ludwig Boltzmann not only showed that his Boltzmann equation, which captures the essence of the second law of thermodynamics in mathematical form, admits James Clerk Maxwell's distribution as an ... More

## Lecture notes on quantum Brownian motion

*László Erdős*

### in Quantum Theory from Small to Large Scales: Lecture Notes of the Les Houches Summer School: Volume 95, August 2010

- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199652495
- eISBN:
- 9780191741203
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199652495.003.0001
- Subject:
- Physics, Atomic, Laser, and Optical Physics

Einstein's kinetic theory of Brownian motion, based upon light water molecules continuously bombarding a heavy pollen, provided an explanation of diffusion from Newtonian mechanics. Since the ... More

## STRONG COUPLING: POLARITON BOSE CONDENSATION

*Alexey V. Kavokin and Jeremy J. Baumberg*

### in Microcavities

- Published in print:
- 2007
- Published Online:
- May 2008
- ISBN:
- 9780199228942
- eISBN:
- 9780191711190
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199228942.003.0008
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This chapter addresses the rich variety of physical effects linked to the Bose-Einstein condensation of exciton-polaritons, including stimulated scattering of exciton-polaritons, spontaneous symmetry ... More

## Relativistic Kinetic Theory

*Yvonne Choquet-Bruhat*

### in General Relativity and the Einstein Equations

- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780199230723
- eISBN:
- 9780191710872
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199230723.003.0010
- Subject:
- Mathematics, Applied Mathematics

This chapter presents the basic equations of the relativistic kinetic theory; it proves local existence theorems for Einstein equations coupled with kinetic matter. It then provides thermodynamic ... More

## The Boltzmann equation

*CARLO CERCIGNANI*

### in Ludwig Boltzmann: The Man Who Trusted Atoms

- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780198570646
- eISBN:
- 9780191717949
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570646.003.0004
- Subject:
- Physics, History of Physics

The problem of irreversibility came to the forefront in kinetic theory with Ludwig Boltzmann. In 1872, Boltzmann not only derived the equation that bears his name, but also introduced a definition of ... More

## Statistical mechanics

*D. Violeau*

### in Fluid Mechanics and the SPH Method: Theory and Applications

- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199655526
- eISBN:
- 9780191741227
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199655526.003.0002
- Subject:
- Physics, Condensed Matter Physics / Materials

The notions of Chapter 1 are extended here to systems of many individuals (thus many degrees of freedom), now seen from a statistical viewpoint. In the phase space, the chapter shows Liouville’s ... More

## The Boltzmann Equation and the H Theorem (1872–1875)

*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/9780198816171.003.0004
- Subject:
- Physics, Atomic, Laser, and Optical Physics, History of Physics

This chapter covers Boltzmann’s writings about the Boltzmann equation and the H theorem in the period 1872–1875, through which he succeeded in deriving the irreversible evolution of the distribution ... More

## Random Processes in Physics and Finance

*Melvin Lax, Wei Cai, and Min Xu*

- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780198567769
- eISBN:
- 9780191718359
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567769.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This book discusses random processes in physics, from basic probability theory to the Fokker-Planck process and Langevin equation for the Fokker Planck process and diffusion. It includes diverse ... More

## FORMAL TRANSPORT THEORY

*J. M. Ziman*

### in Electrons and Phonons: The Theory of Transport Phenomena in Solids

- Published in print:
- 2001
- Published Online:
- September 2007
- ISBN:
- 9780198507796
- eISBN:
- 9780191709937
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507796.003.0007
- Subject:
- Physics, Condensed Matter Physics / Materials

The analysis of the microscopic processes by which electrons and phonons are scattered is only half the calculation of the macroscopic transport coefficients. To discuss the flow of electric and ... More

## A Kinetic-Theory Description of Fluids

*Luciano Rezzolla and Olindo Zanotti*

### in Relativistic Hydrodynamics

- Published in print:
- 2013
- Published Online:
- January 2014
- ISBN:
- 9780198528906
- eISBN:
- 9780191746505
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528906.003.0002
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter illustrates how the foundations of the fluid description are rooted in statistical mechanics and in kinetic theory. This approach, which is appropriate for those systems composed of a ... More

## Kinetic Theory of Granular Gases

*Nikolai V. Brilliantov and Thorsten Pöschel*

- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198530381
- eISBN:
- 9780191713057
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198530381.001.0001
- Subject:
- Physics, Condensed Matter Physics / Materials

Kinetic Theory of Granular Gases provides an introduction to the rapidly developing theory of dissipative gas dynamics — a theory which has mainly evolved over the last decade. The book ... More

## The Boltzmann equation for dilute gases

*Rodrigo Soto*

### in Kinetic Theory and Transport Phenomena

- Published in print:
- 2016
- Published Online:
- June 2016
- ISBN:
- 9780198716051
- eISBN:
- 9780191824401
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198716051.003.0004
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The Boltzmann equation, which is the first and best known kinetic equation, describes the dynamics of classical dilute gases. For its derivation, the motion of the atoms and molecules is separated in ... More

## Diffusive classical transport in two-dimensional electron gases

*Thomas Ihn*

### in Semiconductor Nanostructures: Quantum states and electronic transport

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199534425
- eISBN:
- 9780191715297
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199534425.003.0010
- Subject:
- Physics, Condensed Matter Physics / Materials

Diffusive electronic transport in degenerately doped semiconductors at low magnetic fields can be successfully described within the Drude theory of electrical conduction. This chapter introduces the ... More

## Kinetic theory before Boltzmann

*CARLO CERCIGNANI*

### in Ludwig Boltzmann: The Man Who Trusted Atoms

- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780198570646
- eISBN:
- 9780191717949
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570646.003.0003
- Subject:
- Physics, History of Physics

The first atomic theory is credited to Democritus of Abdera, who lived in the 5th century BC. The actual development of the kinetic theory of gases accordingly took place much later, in the 19th ... More

## Boltzmann’s relation and the statistical interpretation of entropy

*CARLO CERCIGNANI*

### in Ludwig Boltzmann: The Man Who Trusted Atoms

- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780198570646
- eISBN:
- 9780191717949
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570646.003.0006
- Subject:
- Physics, History of Physics

Ludwig Boltzmann first used probabilistic arguments in his answer to Johann Loschmidt's objection to his Boltzmann equation and his assumptions about entropy in the H-theorem. Up to that moment, ... More

## Introduction

*CARLO CERCIGNANI*

### in Ludwig Boltzmann: The Man Who Trusted Atoms

- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780198570646
- eISBN:
- 9780191717949
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570646.003.0013
- Subject:
- Physics, History of Physics

All the fundamental laws of physics are symmetric with respect to the inversion of the time arrow; the cup which reunites itself from the broken pieces, recovers the coffee from the floor and jumps ... More

## Boltzmann Equation

*Nikolai V. Brilliantov and Thorsten Pöschel*

### in Kinetic Theory of Granular Gases

- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198530381
- eISBN:
- 9780191713057
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198530381.003.0006
- Subject:
- Physics, Condensed Matter Physics / Materials

The evolution of the velocity of the distribution function is governed by the Boltzmann equation. This chapter derives the Boltzmann equation for the homogeneous cooling granular gas and discusses ... More

## Transport and evolution of classical and quantum ensembles

*Sandip Tiwari*

### in Semiconductor Physics: Principles, Theory and Nanoscale

- Published in print:
- 2020
- Published Online:
- November 2020
- ISBN:
- 9780198759867
- eISBN:
- 9780191820830
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198759867.003.0008
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter explores the evolution of an ensemble of electrons under stimulus, classically and quantum-mechanically. The classical Liouville description is derived, and then reformed to the quantum ... More