H-theorem

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.

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

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where the function C() represents binary collisions. At equilibrium, $\sigma =0$.

Boltzmann's H-function

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

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where ${\mathbf {V} }$ is the molecular velocity. A restatement of the H-theorem is

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See also

• Boltzmann equation
• Second law of thermodynamics

References

1. L. Boltzmann "", Wiener Ber. 63 pp. 275- (1872)
2. Sybren R. De Groot and Peter Mazur "Non-Equilibrium Thermodynamics", Dover Publications
3. 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)