# Difference between revisions of "H-theorem"

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where the function C() represents binary collisions. | where the function C() represents binary collisions. | ||

At equilibrium, <math>\sigma = 0</math>. | At equilibrium, <math>\sigma = 0</math>. | ||

+ | ==H-function== | ||

+ | Boltzmann's ''H-function'' is defined by (Eq. 5.66 Ref. 3): | ||

+ | |||

+ | :<math>H=\iint f({\mathbf V}, {\mathbf r}, t) \ln f({\mathbf V}, {\mathbf r}, t) ~ d {\mathbf r} d{\mathbf V}</math> | ||

+ | |||

+ | where <math>{\mathbf V}</math> is the molecular velocity. A restatement of the H-theorem is | ||

+ | |||

+ | :<math>\frac{dH}{dt} \leq 0</math> | ||

==See also== | ==See also== | ||

*[[Boltzmann equation]] | *[[Boltzmann equation]] | ||

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# L. Boltzmann "", Wiener Ber. '''63''' pp. 275- (1872) | # L. Boltzmann "", Wiener Ber. '''63''' pp. 275- (1872) | ||

#[http://store.doverpublications.com/0486647412.html Sybren R. De Groot and Peter Mazur "Non-Equilibrium Thermodynamics", Dover Publications] | #[http://store.doverpublications.com/0486647412.html Sybren R. De Groot and Peter Mazur "Non-Equilibrium Thermodynamics", Dover Publications] | ||

+ | #[http://www.oup.com/uk/catalogue/?ci=9780195140187 Robert Zwanzig "Nonequilibrium Statistical Mechanics", Oxford University Press (2001)] | ||

[[category: non-equilibrium thermodynamics]] | [[category: non-equilibrium thermodynamics]] |

## Revision as of 14:07, 24 August 2007

Boltzmann's **H-theorem** states that the entropy of a closed system can only increase in the course of time, and must
approach a limit as time tends to infinity.

where is the *entropy source strength*, given by (Eq 36 Chap IX Ref. 2)

where the function C() represents binary collisions. At equilibrium, .

## H-function

Boltzmann's *H-function* is defined by (Eq. 5.66 Ref. 3):

where is the molecular velocity. A restatement of the H-theorem is

## See also

## References

- L. Boltzmann "", Wiener Ber.
**63**pp. 275- (1872) - Sybren R. De Groot and Peter Mazur "Non-Equilibrium Thermodynamics", Dover Publications
- Robert Zwanzig "Nonequilibrium Statistical Mechanics", Oxford University Press (2001)