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	Onsager, Lars (1903–1976) \| Encyclopedia of Energy
		Onsager was born on November 27, 1903, to Ingrid and Erling Onsager.
		In the derivation, Onsager used the fact that the microscopic dynamics is symmetric in time, and he assumed that microscopic fluctuations on the average follow macroscopic laws when they relax towards equilibrium.
		Although the reciprocal relations, electrolyte theory, and the solution of the Ising model were high-points in Onsager's career, he had broader interests.
	www.bookrags.com /research/onsager-lars-19031976-mee-03 (1388 words)

	Lars Onsager - Wikipedia, the free encyclopedia
		His work at Brown was mainly concerned with the effects on diffusion of temperature gradients, and produced the Onsager reciprocal relations, a set of equations published in 1929 and, in an expanded form, in 1931, in statistical mechanics whose importance went unrecognized for many years.
		This was particularly appropriate because Onsager, like Willard Gibbs, had been primarily involved in the application of mathematics to problems in physics and chemistry and, in a sense, could be considered to be continuing in the same areas where Gibbs had pioneered.
		At age 70, Onsager was involuntarily retired as an emeritus professor at Yale, in 1973.
	en.wikipedia.org /wiki/Lars_Onsager (991 words)

	Onsager reciprocal relations - Wikipedia, the free encyclopedia
		In thermodynamics, the Onsager reciprocal relations express the equality of certain relations between flows and forces in thermodynamical systems out of equilibrium, but where a notion of local equilibrium exists.
		This was shown to be necessary by Lars Onsager using statistical mechanics.
		The theory developed by Onsager is much more general than this example and capable of treating more than two thermodynamic forces at once.
	en.wikipedia.org /wiki/Onsager_reciprocal_relations (326 words)

	Nobel Prize in Chemistry 1968 - Presentation Speech
		Onsager's reciprocal relations can be described as a universal natural law, the scope and importance of which becomes clear only after being put in proper relation to complicated questions in border areas between physics and chemistry.
		Onsager's great contribution was that he could prove that if the equations governing the flows are written in an appropriate form, then there exist certain simple connections between the coefficients in these equations.
		Onsager started from a statistical mechanical calculation of the fluctuations in a system, which could be directly based on the simple laws of motion which are symmetrical with regard to time.
	nobelprize.org /nobel_prizes/chemistry/laureates/1968/press.html (947 words)

	C&EN: SCIENCE & TECHNOLOGY - AN ELECTRIC MOMENT
		Onsager sought to correct this misconception by performing an analysis of the interaction of a dipolar solute molecule with the electric field that is produced as the result of the polarization of the surrounding solvent by the solute molecule."
		Onsager was the first to recognize its significance, and now everyone concerned with solvent effects must include the reaction field in their picture of chemical reaction dynamics in solution.
		Onsager received the 1968 Nobel Prize in Chemistry for other work on the thermodynamics of irreversible processes, which was published in two papers in 1931.
	pubs.acs.org /cen/science/8146/8146jacs125.html (866 words)

	Nat' Academies Press, Biographical Memoirs V.60 (1991)
		Though they arose in Onsager's mind from his studies of electrolytic conduction, he soon recognized their application to the cross-coefficients for the diffusion of pairs of solutes in the same solution (1932,1) and the varied interactions that can occur between thermal conduction, diffusion, and electrical conduction.
		Onsager himself set much store by the Principle of Least Dissipation, which—for systems very close to equilibrium—he showed to be mathematically equivalent to the reciprocal relations.
		The passage of time has perhaps modified this judgment; though the Principle was later generalized by Onsager and Machlup (1953,1,2) and supplied with new theoretical foundations, it does not in fact hold for substantial departures from equilibrium and, in any case, it is the reciprocal relations that are directly accessible to experimental test.
	www.nap.edu /books/0309044421/html/197.html (440 words)

	[No title] (Site not responding. Last check: 2007-10-18)
		Title Criticism of Onsager's reciprocal relations Author Warren D. Smith, NECI Abstract Onsager's second kind of ``reciprocal relations'' %[Phys.Rev. 37 (1931) 405-426; 38 (1931) 2265-2279] state that $\sigma (\vec{H}) = \sigma^{T} (-\vec{H})$ where $\sigma$ is the $3 \times 3$ conductance matrix, $\vec{H}$ is an externally applied magnetic field, and $T$ means matrix transpose.
		We also have counterexamples to the Onsager relations of the first kind (which are the special case $\vec{H}=\vec{0}$).
		Keywords Onsager relation, galvanomagnetic effects, magnetoresistance, non-ohmic resistors, nonlinear electrical materials, chirality, errors in textbooks.
	www.math.temple.edu /~wds/homepage/onsag2.sue (316 words)

	Onsager, Lars
		Onsager was born in Christiania (now Oslo) and studied at Norges Tekniske Høgskole in Trondheim.
		Investigating the connection between microscopic reversibility and transport processes, Onsager found that the key to the problem is the distribution of molecules and energy caused by random thermal motion.
		Using this principle Onsager derived a set of equations known as Onsager's law of reciprocal relations, sometimes called the fourth law of thermodynamics.
	www.cartage.org.lb /en/themes/Biographies/MainBiographies/O/Onsager/1.html (282 words)

	Abstract Nikolaj Walraven (Site not responding. Last check: 2007-10-18)
		In non-equilibrium thermodynamics, however, the formulation of flux-force relations is subject to several disciplinary and constraining principles, which, after being obeyed, deliver some spectacular rewards.
		Onsager’s principle dictates that the matrix of coefficients is symmetrical, that is: the "off-diagonal" coefficients, perpendicular and equidistant to the diagonal, are equal in magnitude and in sign.
		The linearity of the relation between a driving force and a non-conjugated flux (coupled transport process), is guaranteed as long as the corresponding conjugated flux-force relations are linear.
	www.geo.uu.nl /Research/Geochemistry/abstracts/300505_1.html (603 words)

	Lars Onsager Biography \| World of Biology
		Onsager excelled in chemistry from an early age, and his prodigious talent in the field was exhibited while still a student.
		By 1936, Onsager had developed a new model of dipoles that could be used to modify Debye's theory and provide accurate predictions for all cases.
		Onsager and his wife finally did become citizens as the war drew to a close in 1945.
	www.bookrags.com /biography/lars-onsager-wob (1098 words)

	MSU Chemistry - Gallery of Chemists' Photo-Portraits and Mini-Biographies - Individual
		For this discovery of the Onsager reciprocal relations (as they came to be known), mathematical equations fundamental to the thermodynamic theory of irreversible processes, he received the 1968 Nobel Prize in Chemistry.
		In the intervening years and afterward, Onsager made major contributions to varied areas of theoretical physical chemistry: electrolytes, dielectric liquids, isotope separation by diffusion, disordered solids, superfluidity, the behavior of ice as a semi-conductor, and others.
		Onsager was born in Oslo, Norway and studied chemical engineering at the Norges Tekniske Hogskole in Trondheim (Ch.E. At age 22 he detected a flaw in the Debye-Hückel theory; this led to a research assistantship with Debye in Zurich, Switzerland (1925-1928).
	www.chemistry.msu.edu /Portraits/PortraitsHH_Detail.asp?HH_LName=Onsager (251 words)

	Biographical note
		Lars Onsager, Norwegian-American chemist and physicist, was born in Oslo on November 27th 1903 to Erling Onsager, a barrister, and Ingrid, née Kirkeby.
		In 1933 Lars Onsager married the Austrian-born Margarethe Arledter.
		The so-called Onsager reciprocal relations that he derived have been of tremendous importance in a wide range of applications.
	www.ub.ntnu.no /formidl/hist/tekhist/tek5/bibnote.htm (394 words)

	3. The Intrinsic Symmetry of the Physical Properties
		(c) the components of the tensors representing the magneto-electric polarization and reciprocal magneto-electric polarization (eq.
		As has been pointed out the intrinsic symmetry characteristic for the transport processes is the consequence of Onsager's reciprocal relations.
		However, it is important to stress that this relation is valid only if the fluxes and the thermodynamical forces connected with them are suitably selected.
	www.iucr.org /iucr-top/comm/cteach/pamphlets/18/node3.html (917 words)

	THE COLLECTED WORKS OF LARS ONSAGER
		Onsager's scientific achievements were characterized by deep insights into the natural sciences.
		His two best-known accomplishments are his reciprocal relations for irreversible processes, for which he received the 1968 Nobel Prize in Chemistry, and his explicit solution of the two-dimensional Ising model, a mathematical tour de force that created a sensation when it appeared.
		In this volume, Onsager's contributions are divided into the following fields: irreversible processes; the Ising model; electrolytes; colloids; helium II and vortex quantization; off-diagonal long-range order and flux quantization; electrons in metal; turbulence; ion recombination; fluctuation theory; dielectrics; ice and water; biology; Mathieu functions.
	www.worldscibooks.com /physics/3027.html (526 words)

	[No title]
		We derive the fluctuation-dissipation relation and emphasize the important fact that it is a {\em macroscopic relation} independent of many details of the particle system, such as microscopic reversibility.
		Our parameter $\lambda$ is likewise related to the usual electrochemical potential $\mu$ as $\lambda=\beta\mu.$ In Section 4.3 of this paper we shall show that $f$ has a simple operational significance as the minimum energy dissipated by external fields required to change the density from its reference value $n^*$ to a new value.
		The Nyquist relation \cite{35} in electrical circuits between the power spectrum of the noisy EMF (electromotive force) and the frequency-dependent impedance is a prototypical example.
	www.ma.utexas.edu /mp_arc/html/papers/95-168 (11098 words)

	untitled1.html (Site not responding. Last check: 2007-10-18)
		Extension of Onsager's theory of reciprocal relations I. Phys.
		Relations between path integrals and the variational principles of Hamilton.
		The role of Onsager relations in the development of thermodynamics of irreversible processes.
	mazur-www.harvard.edu:16080 /pm/publications.html (1333 words)

	untitled1.html
		Extension of Onsager's theory of reciprocal relations I. Phys.
		Relations between path integrals and the variational principles of Hamilton.
		The role of Onsager relations in the development of thermodynamics of irreversible processes.
	mazur-www.harvard.edu /pm/publications.html (1333 words)

	Criticism of Onsager's reciprocal relations (ResearchIndex) (Site not responding. Last check: 2007-10-18)
		Abstract: Onsager's second kind of "reciprocal relations" state that oe(~ H) = oe T (\Gamma ~ H) where oe is the 3 \Theta 3 conductance matrix, ~ H is an externally applied magnetic field, and T means matrix transpose.
		This is only supposed to hold for "linear" materials for which the current density ~ J is related to the electric field ~ E by h ~ Ji = oe ~ E. This is just one instance of a class of mathematically equivalent but physically different relations; e.g.
		1 Mulley: Photocyclization of stilbenes and related molecules (context) - Mulley - 1984
	citeseer.ist.psu.edu /smith99criticism.html (664 words)

	Thermodynamics
		Thermodynamics (Greek: thermos = heat and dynamic = change) is the physics of energy, heat, work, entropy and the spontaneity of processes.
		Thermodynamics is closely related to statistical mechanics from which many thermodynamic relationships can be derived.
		While dealing with processes in which systems exchange matter or energy, classical thermodynamics is not concerned with the rate at which such processes take place, termed kinetics.
	en.mcfly.org /Thermodynamics (1734 words)

	reviews (Site not responding. Last check: 2007-10-18)
		Subsequently, Lars Onsager used fluctuation theory to demonstrate the famous reciprocal relations that provide the basis for the theory of linear nonequilibrium thermodynamics.
		There is a nice treatment of Gaussian fluctuation theory and a proof of the Onsager reciprocal relations.
		Topics include phenomenological coefficients, Onsager reciprocal relationships, the symmetry principle, thermoelectric phenomena, the Peltier effect, diffusion, heat conduction in anisotropic solids, electrokinetic phenomena, Saxen relationships, nonequilibrium stationary states and their stability, thermal gradients, open chemical systems, electric circuits, and the theorem of minimum entropy production.
	dilip.chem.wfu.edu /reviews.html (1641 words)

	Middle East Open Encyclopedia: Thermodynamics (Site not responding. Last check: 2007-10-18)
		Thermodynamics (from the Greek thermos meaning heat and dynamis meaning power) is a branch of physics that studies the effects of temperature, pressure, and volume changes on physical systems at the macroscopic scale.
		Internal energy is the internal energy of the system, enthalpy is the internal energy of the system plus the energy related to pressure-volume work, and Helmholtz and Gibbs free energy are the energies available in a system to do useful work when the temperature and volume or the pressure and temperature are fixed, respectively.
		In 1875 Austrian physicist Ludwig Boltzmann declared that "the general struggle for existence of animate beings is a struggle for entropy".
	www.baghdadmuseum.org /ref/index.php?title=Thermodynamics (2895 words)

	O - Glossary of chemical terms
		Onsager relations are an important set of equations in the thermodynamics of irreversible processes.
		The theory was developed by the Norwegian chemist Lars Onsager (1903-1976) in 1931.
		Ostwald's dilution law is a relation for the concentration dependence of the molar conductivity Λ of an electrolyte solution, viz.
	www.ktf-split.hr /periodni/en/abc/o.html (641 words)

	[No title] (Site not responding. Last check: 2007-10-18)
		Title Criticism of Onsager's reciprocal relations Author Warren D. Smith, NECI Abstract Onsager's second kind of ``reciprocal relations'' %[Phys.Rev. 37 (1931) 405-426; 38 (1931) 2265-2279] state that $\sigma (\vec{H}) = \sigma^{T} (-\vec{H})$ where $\sigma$ is the $3 \times 3$ conductance matrix, $\vec{H}$ is an externally applied magnetic field, and $T$ means matrix transpose.
		We also have counterexamples to the Onsager relations of the first kind (which are the special case $\vec{H}=\vec{0}$).
		Apparently there have been zero intentional experimental tests (so far) of any Onsager relation in a material inequivalent to its reversal; but I will argue that a 1996 experiment by Solin, Thio, et al.
	math.temple.edu /~wds/homepage/onsag2.sue (316 words)

	The Place of Darcy’s Law in the Framework of Non-Equilibrium Themodynamics
		It was Onsager (1931), who postulated that if one sets every flux appearing in the dissipation equation as a linear homogeneous function of each of the driving forces appearing in that same equation, one finds that the matrix of phenomenological coefficients is symmetrical.
		The equality of the cross-diagonal coefficients is known as Onsager’s Reciprocal Relations.
		The misunderstanding of these coupled transport processes has lead some researchers to erroneously conclude that their observations are “non-Darcian.” The equality of the “twin” coefficients is a welcome bonus in the study of the complexity of transport processes occurring in soils.
	www.pubs.asce.org /WWWdisplay.cgi?0301406 (364 words)

	Lars Onsager
		Lars Onsager was born in Oslo, Norway, November 27, 1903 to parents Erling Onsager, Barrister of the Supreme Court of Norway, and Ingrid, née Kirkeby.
		During this time he gave lectures on statistical mechanics, published the reciprocal relations and made progress on a variety of problems.
		Lars Onsager holds honary degrees of Doctor of Science from Harvard University (1954), Rensselaer Polytechnic Institute (1962), Brown University (1962), Rheinisch-Westfahlische Technische Hochschule (1962), the University of Chicago (1968), Ohio State University (Cleveland, 1969), Cambridge University (1970) and Oxford University (1971), and Doctor Technical from Norges tekniske høgskole (1960).
	home.nvg.org /~endresen/onsager.html (601 words)

	ROBERT ROSEN: THE WELL POSED QUESTION AND
		The modeling relation is based on the universally accepted belief that the world has some sort of order associated with it; it is not a hodge-podge of seemingly random happenings.
		Given the modeling relation and the detailed structural correspondence between our percepts and the formal systems into which we encode them, it is possible to make a dichotomous classification between various models of the real world.
		In this case the equations of motion come from two distinct kinds of information, the constitutive laws relating charge to potential in the elements (resistors, capacitors, inductors, semiconductors) and the specific topology of the network in question which is brought into the formalism along with conservation and closure laws in a manner due to Kirchhoff.
	www.people.vcu.edu /~mikuleck/PPRISS3.html (8752 words)

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