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Topic: Gibbs paradox

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	Gibbs paradox
		Richardson, I. The Gibbs paradox and unidirectional fluxes.
		Gibbs paradox and the notion of construction in thermodynamics and statistic physics.
		Gibbs paradox of entropy of mixing: Experimental facts, its rejection, and the theoretical consequences.
	www.mdpi.org /lin/entropy/gibbs-paradox.htm (0 words)

	Gibbs 1987
		Gibbs claims that 'These results [of Ortony et al.
		The weight of this evidence suggests that it may be premature to accept the relevance hypothesis as a reasonable model of the psychological processes used in working out conversational inferences' (574-5).
		The first is the assumption that mutual beliefs must be represented in a mental model as an infinite series of belief statements'.
	www.sil.org /~radneyr/humanities/Gibbs1987.htm (889 words)

	Physical paradox - Wikipedia, the free encyclopedia
		While many physical paradoxes have accepted resolutions that make them little more than curiosities, others may defy resolution and be the result of an inadequate interpretation of the theory, an assumption about the physical world that is violated, or an indication that the theory inadequately describes the conditions.
		Babinet's paradox is that contrary to naive expectations, the amount of radiation removed from a beam in the diffraction limit is proportional to twice the cross-sectional area.
		This paradox was sometimes used to argue that a homogeneous and isotropic universe as required by the cosmological principle was necessarily finite in extent, but it turns out that there are ways to relax the assumptions in other ways that admit alternative resolutions.
	en.wikipedia.org /wiki/Physical_paradox (2379 words)

	Willard Gibbs - ExampleProblems.com
		Josiah Willard Gibbs (February 11, 1839 – April 28, 1903) was an American mathematical physicist who contributed much of the theoretical foundation that led to the development of chemical thermodynamics and was one of the founders of vector analysis.
		Between 1876 and 1878 Gibbs wrote a series of papers collectively entitled "On the Equilibrium of Heterogeneous Substances", considered one of the greatest achievements in physical science in the 19th century and the foundation of the science of physical chemistry.
		fr:Willard Gibbs nl:Josiah Willard Gibbs ja:ウィラード・ギブズ sl:Josiah Willard Gibbs
	www.exampleproblems.com /wiki/index.php?title=Willard_Gibbs&printable=yes (1159 words)

	Call for Papers for the special issue "Gibbs Paradox
		a paper for the special issue "Gibbs Paradox" of Entropy journal.
		Papers published in Entropy on the topics of Gibbs Paradox
		Entropy Calculation of Reversible Mixing of Ideal Gases Shows Absence of Gibbs Paradox
	www.mdpi.org /entropy/si-gibbs-paradox.htm (216 words)

	Josiah Willard Gibbs Summary
		Gibbs was born in New Haven, Connecticut, to a family of well-known academics.
		Gibbs realized that the opportunities for scientific advancement in the United States were slim, and after three years as a tutor at Yale, he traveled to Europe to continue his education.
		Gibbs declined the offer of a paid appointment at Bowdoin College in 1873, but he was tempted to leave Yale in 1880 when he was invited to join the faculty of the newly-founded Johns Hopkins University in Baltimore.
	www.bookrags.com /Josiah_Willard_Gibbs (6561 words)

	Reference.com/Encyclopedia/Gibbs paradox
		Gibbs Paradox is about the definition of mixing process and the concept of similarity.
		The paradox is resolved by concluding that every particle is indistinguishable from every other particle in the volume, thus you cannot measure entropy by measuring particles as if each were individually identifiable.
		It was resolved by J.W. Gibbs himself, by postulating that the gas particles are in fact indistinguishable.
	www.reference.com /browse/wiki/Gibbs_paradox (1131 words)

	Preface
		Also, this derivation sacrifices the major advantage which Gibbs assigned to his canonical ensemble treatment, namely that the canonical ensemble is equally valid for small and large systems, while the transition from eq.
		0.1 is believed to be correct.[4] Gibbs emphasizes that the canonical ensemble is as useful for systems containing few particles as it is for systems containing many particles, in contrast to the microcanonical ensemble, which is only applicable to many particle systems.
		A good example is the treatment of the so-called Gibbs' Paradox, which is not due to Gibbs and which Gibbs did not view as involving a paradox.
	users.wpi.edu /~phillies/stat1/node1.html (1239 words)

	Gibbs paradox - Wikipedia, the free encyclopedia
		In statistical mechanics, a simple derivation of the entropy of an ideal gas, based on the Boltzmann distribution yields an expression for the entropy which is not an extensive variable as it must be, leading to an apparent paradox known as the Gibbs paradox.
		The paradox is resolved by concluding that every particle is indistinguishable from every other particle in the volume, thus you cannot measure entropy by measuring particles as if each were individually identifiable.
		It was resolved by J.W. Gibbs himself, by postulating that the gas particles are in fact indistinguishable.
	en.wikipedia.org /wiki/Gibbs_paradox (784 words)

	Paradoxes - curiouser.co.uk
		Below is a list of paradoxes which you might be interest to research, some of which may be featured at curiouser.co.uk in due course.
		Low birth weight paradox: low birth weight babies have a higher mortality rate, babies of smoking mothers have lower average birth weight, babies of smoking mothers have a higher mortality rate, but low birth weight babies of smoking mothers have a lower mortality rate than other low birth weight babies.
		Nihilist paradox: if truth does not exist, the statement "truth does not exist" is a truth, thereby proving itself incorrect.
	www.curiouser.co.uk /paradoxes (549 words)

	Blogger: Email Post to a Friend
		Gibbs (1839-1903) lived all of his life in New Haven, Connecticut, a bachelor in his sister's house.
		So modestly did Gibbs absorb these accolades that even his friends were unaware of the honors until they read of them in his obituary.
		Gibbs' physics was the one great cornerstone of 19th century science that survived unscathed the relativity and quantum revolutions of the 20th century.
	www.blogger.com /email-post.g?blogID=7097554&postID=112045446254478923 (345 words)

	Rejection of the Gibbs paradox of mixing entropy (Site not responding. Last check: )
		The result of this solution was known as Gibbs' paradox and has existed for more than 120 years due to an annoying misunderstanding caused by this solution.
		The existence of Gibbs' paradox is strange in classic thermodynamics, because the named paradox does not arise from experimental data, but from equations that contradict the Gibbs¹ equation.
		However, we will be able to solve Gibbs paradox in the frame of the statistical mechanic too.
	www.supelec.fr /lss/MaxEnt2000/htm/Abstracts/tatayn.html (314 words)

	Dub Paradox - Urban music promo & podcast » Brian Gibbs & P.U.S.H. (Site not responding. Last check: )
		gibbs” “brian briangibbs mozaik push baltimore dance group betts manager music soul r&b hiphop performing art dancers singer aberdeen md maryland
		Brian Gibbs is at just 19 years so very talented and his stage presence and personality will take him to the top.
		The guys (& 2 girls) are full of energy and work very hard on their performances, they meet at least twice a week for practice in Harford County, MD to choreograph & prepare for upcoming shows which will take them all over the US.
	www.dubparadox.com /2007/01/12/brian-gibbs-push (276 words)

	Paper presented at Symposium on Frontiers of Chemistry
		The Gibbs paradox statement [1] which has been a very fundamental assumption in statistical mechanics says that the entropy of mixing or assembling to form solid assemblages, liquid and gas mixtures or any other analogous assemblages such as quantum states, decreases discontinuously (Fig.1a) with the increase in the property similarity of the composing individuals [1g].
		Some authors revised the Gibbs paradox statement and argued that the entropy of mixing decreases continuously with the increase in the property similarity of the composing individuals (Fig.1b) [1a,1b,1d].
		The Gibbs entropy additivity principle should be the same in form as the Dalton pressure additivity for ideal gases.
	pages.unibas.ch /mdpi/lin/hongkong/hongkong.htm (840 words)

	[No title]
		This is the origin of the Gibbs `paradox', but he never used that word, for to him it was not a paradox at all!
		In the ensuing discussion Gibbs notes that when two unlike gases mix and the entropy increases there is an implication that the gases in principle could be separated again, bringing them back to their original macroscopic states at the expense of making changes in the external environment.
		But Gibbs also notes that for different gases there is virtually no limit to the resemblance they might have to one another, differing only in some tiny physical detail, and still lead to an entropy of mixing (6-5), independent of those details.
	w3.uwyo.edu /~wtg/Issues/Issues6.html (3001 words)

	Gibbs' Paradox
		The Gibb's paradox says that for classical thermodynamics, entropy is properly an extensive variable of a system (and it is).
		But when we take a given system of n moles of gas and double it's size we find that indeed the energy doubled (another extensive variable), but some of the standard equations for entropy arrive at double the entropy plus an extra amount equal to 2nR(ln2), which is the entropy of mixing.
		I like W. Pauli's comments on the paradox: "...the entropy of a system as a characteristic of its state which (in contradistinction to energy) depends on our knowledge of the system.
	www.physicsforums.com /showthread.php?t=72047 (952 words)

	Citebase - Yet another resolution of the Gibbs paradox: an information theory approach
		The ``Gibbs Paradox'' refers to several related questions concerning entropy in thermodynamics and statistical mechanics: whether it is an extensive quantity or not, how it changes when identical particles are mixed, and the proper way to count states in systems of identical particles.
		Several authors have recognized that the paradox is resolved once it is realized that there is no such thing as the entropy of a system, that there are many entropies, and that the choice between treating particles as being distinguishable or not depends on the resolution of the experiment.
		The purpose of this note is essentially pedagogical; we add to their analysis by examining the paradox from the point of view of information theory.
	www.citebase.org /abstract?id=oai:arXiv.org:cond-mat/0109324 (301 words)

	The Gibbs Paradox - Jaynes (ResearchIndex) (Site not responding. Last check: )
		However, it appears that this has been lost for 100 years, due to some obscurities in Gibbs' style of writing and his failure to include this explanation in his later Statistical Mechanics.
		E.T. Jaynes, The Gibbs paradox, in Maximum Entropy and Bayesian Methods, eds.
		11 the Equilibrium of Heterogeneous Substances (context) - Gibbs - 1961
	citeseer.ist.psu.edu /jaynes96gibbs.html (383 words)

	Gibbs' Paradox
		Instead of V we should see V/N at least for large N. Resolving Gibbs' paradox.
		The problem in Gibbs' paradox arises due to the indistinguishability of the particles.
		What has happened is that we have over counted the possible configurations of the system.
	www.maxwellian.demon.co.uk /art/lnG/Gibbs1.html (0 words)

	Rapidshare Books: Entropy and Energy
		It gives instructive examples from elementary thermodynamics and physico-chemistry and extrapolates the notion to non-standard thermodynamic subjects like shape memory, dissipation of the earth's atmosphere, and sociology.
		The works of the thermodynamic pioneers are presented, in particular Clausius, Caratheodory, Boltzmann, Gibbs, and Planck.
		The laws of thermodynamics and their limitations are discussed; also the pertinacious Gibbs paradox.
	rapidsharebooks.blogspot.com /2007/01/entropy-and-energy.html (256 words)

	gibbs-paradox.htm
		Robert Rosen, The Gibbs Paradox and the Distinguishability of Physical Systems." Philosophy of Science 31: 232-236.
		Drs J.H. van Lith-van Dis "Some common misconceptions regarding the Gibbs paradox", 5th UK conference on mathematical and conceptual foundations of modern physics, Oxford, September 1996.
		Lin SK Gibbs paradox of entropy of mixing: Experimental facts, its rejection and the theoretical consequences
	pages.unibas.ch /mdpi/lin/entropy/gibbs-paradox.htm (772 words)

	[No title]
		In his great work on the equilibrium of heterogeneous systems (1875-1878) Gibbs briefly discussed the entropy of mixing of two ideal gases and, since his statistical mechanics was not yet fully developed, he was discussing only differences in the experimental entropy defined by Clausius:
		What Gibbs sees clearly and emphasizes strongly is that S is both macroscopic and statistical in nature.
		Gibbs, of course, had no way of comprehending this situation, though the specific heat problem had alerted him to the fact that something was wrong (hence his introduction of the factor).
	faraday.uwyo.edu /~tgrandy/Issues/Issues6.html (2686 words)

	The Book of THoTH (Leaves of Wisdom) - Scientific phenomena named after people
		Gibbs free energy, Gibbs paradox, Gibbs' phase rule, Gibbs phenomenon – Josiah Willard Gibbs
		Gibbs-Helmholtz equation – Josiah Willard Gibbs and Hermann von Helmholtz
		Kochen-Specker paradox – Simon Kochen and Ernst Specker
	www.book-of-thoth.com /thebook/index.php/Scientific_phenomena_named_after_people (2042 words)

	Maxwell's Demon and Gibbs's Paradox
		Gibbs's paradox arises from the way in which the number of accessible states of a gas is calculated in classical mechanics.
		This reduces the number of accessible states by N!, yielding an equation for the entropy which eliminates the ``paradox.'' This modification is justified by quantum mechanics; however, it is possible to resolve the paradox in another, purely classical manner.
		, which is exactly enough to counterbalance the decrease in entropy of the gas in the Gibbs's paradox.
	users.ntsource.com /~neilsen/papers/demon/node6.html (0 words)

	The KLI Theory Lab - keywords - physical systems
		Rosen, R. The Gibbs paradox and the distinguishability of physical systems.
		Keywords: Gibbs paradox • identity • physical systems.
		Van der Meer, J.M. The engagement of religion and biology: A case study in the mediating role of metaphor in the sociobiology of Lumsden & Wilson.
	www.kli.ac.at /theorylab/Keyword/P/PhyslSys.html (125 words)

	Usenet Physics FAQ
		The web version was created, maintained and enlarged by Michael Weiss and Philip Gibbs.
		Others who have written for the FAQ are credited at the top of the items they submitted while many more who have made smaller contributions have been thanked privately.
		Thanks go to John Baez, Jay Brown, Jon Butterworth, Alan Cairns, Dave Edsall, Harald Falkenberg, Philip Gibbs, Chung-rui Kao, Matthew Parry, Johan Wevers, and the various organisations for hosting us!
	math.ucr.edu /home/baez/physics (0 words)

	Subfaculteit Wijsbegeerte - Janneke van Lith
		thesis: "De paradox van Gibbs" [The Gibbs paradox] (supervisor: Dr J. Uffink; thesis in Dutch).
		"A solution to the ‘paradox of the constancy of the fine-grained entropy’;", 7th UK conference on mathematical and conceptual foundations of modern physics, Nottingham, September 1998.
		"Some common misconceptions regarding the Gibbs paradox", 5th UK conference on mathematical and conceptual foundations of modern physics, Oxford, September 1996.
	www.phil.uu.nl /~lith/CV.shtml (673 words)

	[No title]
		The maximal amount of extractable work is a new quantity, called ergotropy, and it has a simple explantion: in the optimal final state is the largest amount of particles is in the ground state, the one-but-largest in the first-excited state, and so on [L45].
		The paradox lies in the discontinuity: there is an increase no matter how small the difference between the gases, but not when they are equal.
		It was believed to be solved by the quantum mixing entropy argument, but that was shown to create a new problem at almost the same spot: it is a neither operational.
	staff.science.uva.nl /~nieuwenh/QL2L.html (1464 words)

	[No title]
		Denbigh, K.G. and M.L.G. Redhead (1989), ``Gibbs' Paradox and Non-Uniform Convergence,'' Synthese 81, 283.
		Gibbs, J.W. (1875), ``On the Equilibrium of Heterogeneous Substances,'' Trans.
		(1992), ``The Gibbs Paradox,'' in Maximum Entropy and Bayesian Methods, C.R. Smith, G.J. Erickson, and P.O Neudorfer (eds.), Kluwer, Dordrecht.
	faraday.uwyo.edu /~tgrandy/Issues/Refs.html (1124 words)

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