H-theorem: Difference between revisions

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{{Stub-general}}
==Boltzmann's 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
Boltzmann's '''H-theorem''' states that the [[entropy]] of a closed system can only increase in the course of time, and must
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#[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)]
#[http://www.oup.com/uk/catalogue/?ci=9780195140187  Robert Zwanzig "Nonequilibrium Statistical Mechanics", Oxford University Press (2001)]
'''Related reading'''
*[http://dx.doi.org/10.1073/pnas.1001185107  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)]
*[http://dx.doi.org/10.1063/1.3675847 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)]
[[category: non-equilibrium thermodynamics]]
[[category: non-equilibrium thermodynamics]]

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Boltzmann's H-theorem[edit]

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[edit]

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[edit]

See also[edit]

References[edit]

  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