H-theorem - Revision history

Carl McBride: /* References */ Added a recent publication

2012-01-13T16:01:15Z

References: Added a recent publication

← Older revision		Revision as of 18:01, 13 January 2012
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	'''Related reading'''		'''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/10.1073/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]]

2010-05-19T10:01:04Z

References: Added a recent publication

← Older revision		Revision as of 12:01, 19 May 2010
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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)]

	[[category: non-equilibrium thermodynamics]]		[[category: non-equilibrium thermodynamics]]

2007-10-16T18:10:46Z

← Older revision		Revision as of 20:10, 16 October 2007
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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

2007-09-04T09:44:03Z

← Older revision		Revision as of 11:44, 4 September 2007
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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		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.		approach a limit as time tends to infinity.
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	where the function C() represents binary collisions.		where the function C() represents binary collisions.
	At equilibrium, <math>\sigma = 0</math>.		At equilibrium, <math>\sigma = 0</math>.
	==H-function==		==Boltzmann's H-function==
	Boltzmann's ''H-function'' is defined by (Eq. 5.66 Ref. 3):		Boltzmann's ''H-function'' is defined by (Eq. 5.66 Ref. 3):

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	:<math>\frac{dH}{dt} \leq 0</math>		:<math>\frac{dH}{dt} \leq 0</math>
			==Gibbs's H-function==
	==See also==		==See also==
	*[[Boltzmann equation]]		*[[Boltzmann equation]]

2007-08-24T12:07:54Z

← Older revision		Revision as of 14:07, 24 August 2007
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	where the function C() represents binary collisions.		where the function C() represents binary collisions.
	At equilibrium, <math>\sigma = 0</math>.		At equilibrium, <math>\sigma = 0</math>.
			==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>
	==See also==		==See also==
	*[[Boltzmann equation]]		*[[Boltzmann equation]]
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	# L. Boltzmann "", Wiener Ber. '''63''' pp. 275- (1872)		# 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://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)]
	[[category: non-equilibrium thermodynamics]]		[[category: non-equilibrium thermodynamics]]

2007-08-22T10:17:36Z

← Older revision		Revision as of 12:17, 22 August 2007
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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==

2007-08-22T10:11:45Z

@@ Line 1: / Line 1: @@
 ==References==
 # L. Boltzmann "", Wiener Ber. '''63''' pp. 275- (1872)
 [[category: non-equilibrium thermodynamics]]

2007-07-03T10:45:34Z

New page: ==References== # L. Boltzmann "", Wiener Ber. '''63''' pp. 275- (1872) category: non-equilibrium thermodynamics

New page

==References==
# L. Boltzmann "", Wiener Ber. '''63''' pp. 275- (1872)
[[category: non-equilibrium thermodynamics]]