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

Subjects I'm working on- <br style="clear:both;" />

References {{note_label|Wood1992||}} {{ref_harvard|Wood1992|Wood, 1992|}}

equivlist

Template talk:probability distribution#Status of usage
Template talk:Prettytable and MediaWiki talk:Common.css
verify μ is mode of Levy distribution
Combine Heavy tail distribution and Long tail
Mutation-selection balance | Quasispecies model | http://www.biomedcentral.com/1471-2148/5/44

1 Thermodynamics
2 Chi-square distributions
3 Heavy tail distributions
4 Statistical Mechanics
5 Continuum mechanics
6 Work pages

[edit] Chi-square distributions

distribution	$σ 2$	$ν$
scale-inverse-chi-square distribution	$σ 2$	$ν$
inverse-chi-square distribution 1	$1 / ν$	$ν$
inverse-chi-square distribution 2	$1$	$ν$
inverse gamma distribution	$β / α$	$2α$
Levy distribution	$c$	$1$

[edit] Heavy tail distributions

Heavy tail distributions

Distribution	character	$α$
Levy skew alpha-stable distribution	continuous, stable	$0\le \alpha < 2$
Cauchy distribution	continuous, stable	$1$
Voigt distribution	continuous	$1$
Levy distribution	continuous, stable	$1 / 2$
scale-inverse-chi-square distribution	continuous	$ν / 2 > 0$
inverse-chi-square distribution	continuous	$ν / 2 > 0$
inverse gamma distribution	continuous	$α > 0$
Pareto distribution	continuous	$k > 0$
Zipf's law	discrete	$s - 1 > - 1???$
Zipf-Mandelbrot law	discrete	$s - 1 > - 1???$
Zeta distribution	discrete	$s - 1 > - 1???$
Student's t-distribution	continuous	$ν > 0$
Yule-Simon distribution	discrete	$ρ$
? distribution	continuous	$s - 1 > - 1???$
Log-normal distribution???	continuous	$ρ$
Weibull distribution???	?	$?$
Gamma-exponential distribution???	?	$?$

**A Table of Statistical Mechanics Articles**
	Maxwell Boltzmann	Bose-Einstein	Fermi-Dirac
Particle		Boson	Fermion
Statistics	Partition function Identical particles#Statistical properties Statistical ensemble\|Microcanonical ensemble \| Canonical ensemble \| Grand canonical ensemble
Statistics	Maxwell-Boltzmann statistics Maxwell-Boltzmann distribution Boltzmann distribution Derivation of the partition function Gibbs paradox	Bose-Einstein statistics	Fermi-Dirac statistics
Thomas-Fermi approximation	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
Chemical Equilibrium	Classical Chemical equilibrium

[edit] Continuum mechanics

http://online.physics.uiuc.edu/courses/phys598OS/fall04/lectures/

[edit] Work pages

To fix:

Degenerate distribution
Fermi-Dirac statistics - not continuous, necessarily
Bose gas (derive critical temperature)
Spectral density-SPD Cat:Physics = Power spectrum-Cat:signal processing

(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 T_j reservoir, transferring energy dQ_j to the latter. From the above definition of temperature, the energy extracted from the T₀ reservoir by the j-th cycle is

$dQ_{0,j} = T_0 \frac{dQ_j}{T_j} \,\!$

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,

$W = \sum_{j=1}^N dQ_{0,j} = T_0 \sum_{j=1}^N \frac{dQ_j}{T_j} \,\!$

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

$\sum_{i=1}^N \frac{dQ_i}{T_i} \le 0 \,\!$

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

$\sum_{i=1}^N \frac{dQ_i}{T_i} = 0 \,\!$ (reversible cycles)

In mathematics, it is often desireable to express a functional relationship $f(x)\,$ 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 $f^\star(y)\,$ and is called the Legendre transform of the original function.