Editing H-theorem

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==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. 

:<math>\sigma \geq 0</math>

where <math>\sigma</math> is the ''entropy source strength'', given by (Eq 36 Chap IX Ref. 2)

:<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>.
==Boltzmann's 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>
==Gibbs's H-function==
==See also==
*[[Boltzmann equation]]
*[[Second law of thermodynamics]]
==References==
# 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://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)]

[[category: non-equilibrium thermodynamics]]