User:PAR

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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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Help:Displaying a formula

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  • References (Harvard with pages)
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==References==
{{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


Thermodynamics[edit]

Chi-squared distributions[edit]

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

Heavy tail distributions[edit]

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[edit]

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

Others:

Continuum mechanics[edit]

Work pages[edit]

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.

References

  1. ^ Herrmann, F.; Würfel, P. (2005). "Light with nonzero chemical potential". Am. J. Phys. American Association of Physics Teachers. 78 (3): 717–721. doi:10.1119/1.1904623. Retrieved 2012-12-20.  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.
Wall (Impermeable)
Rigid T-Ins No IW External
δQh δWx dT dS dP dV dN dV=0 δQh=0 δWx=0
Process
    Isobaric process - - - - 0 - 0 no - - constant pressure reservoir
    Isochoric process - - - - - 0 0 - yes - -
    Isothermal process - - 0 - - - 0 - no - constant temperature reservoir
    Isentropic process 0 0 - 0 - - 0 - yes yes -
    Adiabatic process 0 - - - - - 0 - yes - -
x-Isolated System
    Mechanically Is. (Guha) - - - - - 0 0 yes - - -
    Adiabatic Is 0 - - - - - 0 - yes - -
    Thermally Is. 0 0 - 0 - - 0 - yes yes -
    Closed system - - - - - - 0 - - - -
    Isolated system 0 0 - 0 - 0 0 yes yes yes -
    Open system - - - - - - - no no no -
Conserved Thermodynamic potential
    U: Internal energy 0 0 - 0 - 0 0 yes yes yes -
    F: Helmholtz free energy - - 0 - - 0 0 yes no - constant temperature reservoir
    H: Enthalpy 0 0 - 0 0 - 0 no yes yes constant pressure reservoir
    G: Gibbs free energy - - 0 - 0 - 0 no no - constant pressure and temperature reservoir

δQh is heat, δWx is irreversible work, so TdS=δQh+δWx. If both are zero, then dS=0. For the 3 possible walls, "T ins" means thermally insulated, and "No IW" means no irreversible work. "External" specifies the region external to the system.