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A barnstar for your extensive contributions to articles related to statistical mechanics! --HappyCamper

Subjects I'm working on- Wikipedia:Writing better articles

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  • References {{note_label|Wood1992||}} {{ref_harvard|Wood1992|Wood, 1992|}}
  • References <ref name="???">reference</ref>,<ref name="???"/>,<references/>,{{rp|p.103}}
  • References (Harvard with pages)
<ref name="Rybicki 1979 22">{{harvnb|Rybicki|Lightman|1979|p=22}}</ref>
{{Reflist|# of columns}} 
=== Bibliography ===
{{ref begin}}
*{{Cite book|etc |ref=harv}}
{{ref end}}

  1. History of Wayne, NY
  2. Australian Trilobite Jump table
  3. RGB
  4. -
  5. Pigment-loss color blindness
  6. Peach
  7. Work7
  8. Work8
  9. Work9
  10. Work10
  11. Elastic Moduli


Chi-squared distributions

scale-inverse-chi-squared distribution
inverse-chi-squared distribution 1
inverse-chi-squared distribution 2
inverse gamma distribution
Levy distribution

Heavy tail distributions

Heavy tail distributions

Distribution character
Levy skew alpha-stable distribution continuous, stable
Cauchy distribution continuous, stable
Voigt distribution continuous
Levy distribution continuous, stable
scale-inverse-chi-squared distribution continuous
inverse-chi-squared distribution continuous
inverse gamma distribution continuous
Pareto distribution continuous
Zipf's law discrete
Zipf-Mandelbrot law discrete
Zeta distribution discrete
Student's t-distribution continuous
Yule-Simon distribution discrete
? distribution continuous
Log-normal distribution??? continuous
Weibull distribution??? ?
Gamma-exponential distribution??? ?

Statistical Mechanics

A Table of Statistical Mechanics Articles
Maxwell Boltzmann Bose-Einstein Fermi-Dirac
Particle Boson Fermion

Partition function
Identical particles#Statistical properties
Statistical ensemble|Microcanonical ensemble | Canonical ensemble | Grand canonical ensemble


Maxwell-Boltzmann statistics
Maxwell-Boltzmann distribution
Boltzmann distribution
Derivation of the partition function
Gibbs paradox

Bose-Einstein statistics Fermi-Dirac statistics
gas in a box
gas in a harmonic trap
Gas Ideal gas

Bose gas
Bose-Einstein condensate
Planck's law of black body radiation

Fermi gas
Fermion condensate

Classical Chemical equilibrium


Continuum mechanics

Work pages

To fix:

(subtract mean) (no subtract mean)
Covariance Correlation
Cross covariance Cross correlation see ext
Autocovariance Autocorrelation
Covariance matrix Correlation matrix
Estimation of covariance matrices

Proof: Introduce an additional heat reservoir at an arbitrary temperature T0, as well as N cycles with the following property: the j-th such cycle operates between the T0 reservoir and the Tj reservoir, transferring energy dQj to the latter. From the above definition of temperature, the energy extracted from the T0 reservoir by the j-th cycle is

Now consider one cycle of the heat engine, accompanied by one cycle of each of the smaller cycles. At the end of this process, each of the N reservoirs have zero net energy loss (since the energy extracted by the engine is replaced by the smaller cycles), and the heat engine has done an amount of work equal to the energy extracted from the T0 reservoir,

If this quantity is positive, this process would be a perpetual motion machine of the second kind, which is impossible. Thus,

Now repeat the above argument for the reverse cycle. The result is

(reversible cycles)

In mathematics, it is often desireable to express a functional relationship as a different function, whose argument is the derivative of f , rather than x . If we let y=df/dx  be the argument of this new function, then this new function is written and is called the Legendre transform of the original function.


  1. {{#invoke:Citation/CS1|citation |CitationClass=journal }} A necessary condition for Planck's law to hold is that the photon number is not conserved, implying that the chemical potential of the photons is zero. While this may be unavoidably true on very long timescales, there are many practical cases that are dealt with by assuming a nonzero chemical potential, which yields an equilibrium distribution which is not Planckian.