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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


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


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


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


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


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


TRANSPORT PROPERTIES OF CHARGE CARRIERS AT LOW TEMPERATURE

A.F. Borghesani

in Ions and electrons in liquid helium

Published in print:
2007
Published Online:
January 2008
ISBN:
9780199213603
eISBN:
9780191707421
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213603.003.0005
Subject:
Physics, Condensed Matter Physics / Materials

This chapter describes the main experimental techniques used to measure the drift velocity in superfluid 4He at low temperature. The experimental results are then presented by showing the ... More


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