H-theorem: Difference between revisions

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:<math>\sigma = -k \sum_{i,j} \int C(f_i,f_j) \ln f_i d {\mathbf u}_i</math>
:<math>\sigma = -k \sum_{i,j} \int C(f_i,f_j) \ln f_i d {\mathbf u}_i</math>


where the function C() represents binary collisions.
At equilibrium, <math>\sigma = 0</math>.
At equilibrium, <math>\sigma = 0</math>.
==See also==
==See also==

Revision as of 11:17, 22 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, .

See also

References

  1. L. Boltzmann "", Wiener Ber. 63 pp. 275- (1872)
  2. Sybren R. De Groot and Peter Mazur "Non-Equilibrium Thermodynamics", Dover Publications