# H-theorem

## Contents

## Boltzmann's H-theorem

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, .

## Boltzmann's 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

## Gibbs's H-function

## 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)

**Related reading**

- Philip T. Gressman and Robert M. Strain "Global classical solutions of the Boltzmann equation with long-range interactions", Proceedings of the National Academy of Sciences of the United States of America
**107**pp. 5744-5749 (2010) - James C. Reid, Denis J. Evans, and Debra J. Searles "Communication: Beyond Boltzmann's H-theorem: Demonstration of the relaxation theorem for a non-monotonic approach to equilibrium", Journal of Chemical Physics
**136**021101 (2012)