Statistical mechanics: Difference between revisions
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Carl McBride (talk | contribs) (Added a quote by David L. Goodstein) |
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<blockquote>''"Ludwig Boltzmann, who spent much of his life studying statistical mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics."'' | |||
:David L. Goodstein "States of Matter" Prentice-Hall (1975) ISBN 978-0138435578 (Chapter 1 page 1).</blockquote> | |||
{{columns-list|3| | |||
==B== | ==B== | ||
*[[BBGKY hierarchy]] | *[[BBGKY hierarchy]] | ||
*[[Boltzmann average]] | |||
*[[Boltzmann constant]] | *[[Boltzmann constant]] | ||
*[[Boltzmann distribution]] | *[[Boltzmann distribution]] | ||
| Line 11: | Line 15: | ||
*[[Chemical potential]] | *[[Chemical potential]] | ||
*[[Compressibility equation]] | *[[Compressibility equation]] | ||
*[[ | *[[Critical exponents]] | ||
*[[Critical points]] | *[[Critical points]] | ||
*[[Curie's law]] | *[[Curie's law]] | ||
==D== | ==D== | ||
*[[Darwin-Fowler method]] | |||
*[[de Broglie thermal wavelength]] | *[[de Broglie thermal wavelength]] | ||
==E== | ==E== | ||
*[[Energy equation]] | *[[Energy equation]] | ||
*[[Entropy]] | *[[Entropy]] | ||
*[[Ensembles in thermostatistics]] | |||
*[[Ergodic hypothesis]] | |||
==F== | ==F== | ||
*[[Fermi-Pasta-Ulam experiment]] | |||
*[[Fisher–Ruelle stability criteria]] | |||
*[[Fisher-Widom line]] | |||
*[[Four-body function]] | *[[Four-body function]] | ||
*[[Frenkel line]] | |||
==G== | ==G== | ||
*[[Gibbs distribution]] | *[[Gibbs distribution]] | ||
*[[Gibbs ensemble]] | *[[Gibbs ensemble]] | ||
*[[Gibbs measures]] | |||
*[[Gibbs paradox]] | *[[Gibbs paradox]] | ||
*[[Goldstone modes]] | *[[Goldstone modes]] | ||
*[[Grand canonical ensemble]] | *[[Grand canonical ensemble]] | ||
==I== | ==I== | ||
*[[Information theory]] | |||
*[[Internal energy]] | *[[Internal energy]] | ||
*[[Intermolecular pair potential]] | *[[Intermolecular pair potential]] | ||
*[[Isoenthalpic–isobaric ensemble]] | |||
*[[Isothermal-isobaric ensemble]] | *[[Isothermal-isobaric ensemble]] | ||
==J== | ==J== | ||
| Line 35: | Line 54: | ||
==K== | ==K== | ||
*[[Kirkwood superposition approximation]] | *[[Kirkwood superposition approximation]] | ||
*[[Kolmogorov–Arnold–Moser theorem]] | |||
==L== | ==L== | ||
*[[Law of corresponding states]] | *[[Law of corresponding states]] | ||
*[[Liouville's theorem]] | *[[Liouville's theorem]] | ||
*[[Loschmidt's paradox]] (Umkehreinwand) | |||
*[[Lyapunov exponents]] | *[[Lyapunov exponents]] | ||
==M== | ==M== | ||
*[[MaxEnt thermodynamics]] | |||
*[[Maxwell velocity distribution]] | *[[Maxwell velocity distribution]] | ||
*[[Maxwell's demon]] | |||
*[[Mean field models]] | |||
*[[Melting curve]] | |||
*[[Microcanonical ensemble]] | *[[Microcanonical ensemble]] | ||
*[[Microstate]] | |||
*[[Mixing systems]] | |||
==P== | ==P== | ||
*[[Pair distribution function]] | *[[Pair distribution function]] | ||
| Line 49: | Line 78: | ||
*[[Phase space]] | *[[Phase space]] | ||
*[[Phase transitions]] | *[[Phase transitions]] | ||
*[[Poincaré theorem]] | |||
*[[Pressure]] | *[[Pressure]] | ||
*[[Pressure equation]] (aka. virial equation) | *[[Pressure equation]] (aka. virial equation) | ||
==Q== | ==Q== | ||
*[[Quantum statistics]] | *[[Quantum statistics]] | ||
==R== | ==R== | ||
*[[Radial distribution function]] | *[[Radial distribution function]] | ||
*[[Ross melting rule]] | |||
==S== | ==S== | ||
*[[Semi-grand ensembles]] | *[[Semi-grand ensembles]] | ||
*[[Stochastic transition]] | |||
*[[Structure factor]] | *[[Structure factor]] | ||
*[[Surface tension]] | *[[Surface tension]] | ||
==T== | ==T== | ||
*[[Temperature]] | *[[Temperature]] | ||
*[[Thermodynamic limit]] | *[[Thermodynamic limit]] | ||
*[[Transfer matrices]] | |||
==W== | |||
*[[Widom line]] | |||
*[[Wigner's distribution function]] | |||
==Y== | |||
*[[Yang-Yang anomaly]] | |||
==Z== | ==Z== | ||
*[[Zermelo’s paradox]] | *[[Zermelo’s paradox]] (Wiederkehreinwand) | ||
}} | |||
==General | ==General reading== | ||
'''Books''' | |||
* Donald A. McQuarrie "Statistical Mechanics", University Science Books (1984) (Re-published 2000) ISBN 978-1-891389-15-3 | |||
* L. D. Landau and E. M. Lifshitz "Statistical Physics", Course of Theoretical Physics volume 5 Part 1 3rd Edition (1984) ISBN 0750633727 | |||
* Terrell L. Hill "Statistical Mechanics: Principles and Selected Applications" (1956) ISBN 0486653900 | |||
* Terrell L. Hill "An Introduction to Statistical Thermodynamics" (1986) ISBN 0486652424 | |||
* Arieh Ben-Naim " Statistical Thermodynamics With Applications to the Life Sciences", World Scientific Publishing (2014) ISBN 978-981-4579-15-5 | |||
'''Papers''' | |||
*[http://dx.doi.org/10.1103/RevModPhys.27.289 D. Ter Haar "Foundations of Statistical Mechanics", Reviews of Modern Physics '''27''' pp. 289 - 338 (1955)] | *[http://dx.doi.org/10.1103/RevModPhys.27.289 D. Ter Haar "Foundations of Statistical Mechanics", Reviews of Modern Physics '''27''' pp. 289 - 338 (1955)] | ||
*[http://dx.doi.org/10.1088/0034-4885/42/12/002 O. Penrose "Foundations of statistical mechanics", Reports on Progress in Physics '''42''' pp. 1937-2006 (1979)] | *[http://dx.doi.org/10.1088/0034-4885/42/12/002 O. Penrose "Foundations of statistical mechanics", Reports on Progress in Physics '''42''' pp. 1937-2006 (1979)] | ||
| Line 72: | Line 119: | ||
*[http://dx.doi.org/10.1016/S0378-4371(98)00517-2 Elliott H. Lieb "Some problems in statistical mechanics that I would like to see solved", Physica A '''263''' pp. 491-499 (1999)] | *[http://dx.doi.org/10.1016/S0378-4371(98)00517-2 Elliott H. Lieb "Some problems in statistical mechanics that I would like to see solved", Physica A '''263''' pp. 491-499 (1999)] | ||
*[http://www.pro-physik.de/Phy/pdfstart.do?mid=3&articleid=25753&recordid=25793 Joel L. Lebowitz "Emergent Phenomena", Physik Journal '''6''' #9 pp. 41-46 (2007)] | *[http://www.pro-physik.de/Phy/pdfstart.do?mid=3&articleid=25753&recordid=25793 Joel L. Lebowitz "Emergent Phenomena", Physik Journal '''6''' #9 pp. 41-46 (2007)] | ||
[[category: statistical mechanics]] | [[category: statistical mechanics]] | ||
__NOTOC__ | __NOTOC__ | ||
Latest revision as of 10:46, 12 January 2020
"Ludwig Boltzmann, who spent much of his life studying statistical mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics."
- David L. Goodstein "States of Matter" Prentice-Hall (1975) ISBN 978-0138435578 (Chapter 1 page 1).
B
- BBGKY hierarchy
- Boltzmann average
- Boltzmann constant
- Boltzmann distribution
- Boltzmann factor
- Born-Green equation
- Brownian motion
C
- Canonical ensemble
- Chemical potential
- Compressibility equation
- Critical exponents
- Critical points
- Curie's law
D
E
F
- Fermi-Pasta-Ulam experiment
- Fisher–Ruelle stability criteria
- Fisher-Widom line
- Four-body function
- Frenkel line
G
- Gibbs distribution
- Gibbs ensemble
- Gibbs measures
- Gibbs paradox
- Goldstone modes
- Grand canonical ensemble
I
- Information theory
- Internal energy
- Intermolecular pair potential
- Isoenthalpic–isobaric ensemble
- Isothermal-isobaric ensemble
J
K
L
- Law of corresponding states
- Liouville's theorem
- Loschmidt's paradox (Umkehreinwand)
- Lyapunov exponents
M
- MaxEnt thermodynamics
- Maxwell velocity distribution
- Maxwell's demon
- Mean field models
- Melting curve
- Microcanonical ensemble
- Microstate
- Mixing systems
P
- Pair distribution function
- Parrondo's paradox
- Partition function
- Phase space
- Phase transitions
- Poincaré theorem
- Pressure
- Pressure equation (aka. virial equation)
Q
R
S
T
W
Y
Z
- Zermelo’s paradox (Wiederkehreinwand)
General reading[edit]
Books
- Donald A. McQuarrie "Statistical Mechanics", University Science Books (1984) (Re-published 2000) ISBN 978-1-891389-15-3
- L. D. Landau and E. M. Lifshitz "Statistical Physics", Course of Theoretical Physics volume 5 Part 1 3rd Edition (1984) ISBN 0750633727
- Terrell L. Hill "Statistical Mechanics: Principles and Selected Applications" (1956) ISBN 0486653900
- Terrell L. Hill "An Introduction to Statistical Thermodynamics" (1986) ISBN 0486652424
- Arieh Ben-Naim " Statistical Thermodynamics With Applications to the Life Sciences", World Scientific Publishing (2014) ISBN 978-981-4579-15-5
Papers
- D. Ter Haar "Foundations of Statistical Mechanics", Reviews of Modern Physics 27 pp. 289 - 338 (1955)
- O. Penrose "Foundations of statistical mechanics", Reports on Progress in Physics 42 pp. 1937-2006 (1979)
- P. W. Anderson "More Is Different", Science 177 pp. 393-396 (1972)
- J. S. Rowlinson "The evolution of some statistical mechanical ideas", Molecular Physics 104 pp. 3399 - 3410 (2006)
- Elliott H. Lieb "Some problems in statistical mechanics that I would like to see solved", Physica A 263 pp. 491-499 (1999)
- Joel L. Lebowitz "Emergent Phenomena", Physik Journal 6 #9 pp. 41-46 (2007)