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Topic: Boltzmann relation

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	Boltzmann's Work in Statistical Physics (Stanford Encyclopedia of Philosophy)
		However, Boltzmann's ideas on the precise relationship between the thermodynamical properties of macroscopic bodies and their microscopic constitution, and the role of probability in this relationship are involved and differed quite remarkably in different periods of his life.
		Boltzmann is often portrayed as a staunch defender of the atomic view of matter, at a time when the dominant opinion in the German-speaking physics community, led by influential authors like Mach and Ostwald, disapproved of this view.
		Actually, Boltzmann's subsequent work in gas theory in the next decade and a half was predominantly concerned with technical applications of his 1872 Boltzmann equation, in particular to gas diffusion and gas friction.
	plato.stanford.edu /entries/statphys-Boltzmann (12999 words)

	Congruence relation Encyclopedia (Site not responding. Last check: )
		In mathematics and especially in abstract algebra, a congruence relation or simply congruence is an equivalence relation that is compatible with some algebraic operation(s).
		The idea is generalized in universal algebra: A congruence relation on an algebra A is a subset of the direct product A × A that is both an equivalence relation on A and a subalgebra of A × A.
		A similar trick allows one to speak of kernels in ring theory as ideals instead of congruence relations, and in module theory as submodules instead of congruence relations.
	www.hallencyclopedia.com /topic/Congruence_relation.html (802 words)

	Boltzmann relation - Wikipedia, the free encyclopedia
		In a plasma, the Boltzmann relation connects the electron density n
		If the ion density is known and the assumptions hold sufficiently well, the electric potential can be calculated simply from the Boltzmann relation.
		Discrepancies with the Boltzmann relation can occur, for example, when oscillations occur so fast that the electrons cannot find a new equilibrium (see e.g.
	en.wikipedia.org /wiki/Boltzmann_relation (187 words)

	A Short History of Vacuum Terminology and Technology--SOUTHERN PVD Co., Ltd
		Ludwig Eduard Boltzmann was born February 20, 1844, in Vienna and died on September 5, 1906, in Duino, Italy.
		Boltzmann was also one of the first Europeans to recognize the importance of the electromagnetic theory proposed by James Clerk Maxwell of England.
		This empirical relation, formulated by Boyle in 1662, states that the pressure (p) of a gas varies inversely as its volume (v) at constant temperature; in equation form, pv=k, and is a constant.
	www.southern-pvd.com /vk/evksh01.htm (2704 words)

	Boltzmann: a disordered genius (April 1999) - Physics World - PhysicsWeb
		Although Boltzmann's first scientific paper was on electrodynamics, his second was devoted to the mechanical meaning of the second law of thermodynamics - a topic that Boltzmann would return to again and again throughout his life, and to which he eventually gave an exhaustive answer.
		Boltzmann wrote to his mother in Vienna in September 1872 saying that he had given a lecture on the theorem to the Physical Society in Berlin, but that hardly anyone was able to follow him - apart from Helmholtz, with whom an interesting discussion developed.
		Boltzmann developed his statistical interpretation of the second law of thermodynamics in his famous paper of 1877 on the second law and probability calculus.
	physicsweb.org /articles/world/12/4/10 (1355 words)

	Basic definitions and thermodynamics
		Boltzmann identified this quantity as the entropy, S of the system, which, for the microcanonical ensemble is a natural function of N, V and E:
		The importance of Boltzmann's relation is that it establishes a connection between the thermodynamic properties of a system and its microscopic details.
		Of course, the ultimate test of Boltzmann's relation between entropy and the partition function is that the above relations correctly generate the known thermodynamic properties of a given system, e.g.
	www.nyu.edu /classes/tuckerman/stat.mech/lectures/lecture_2/node6.html (622 words)

	Springer Online Reference Works
		Boltzmann considered a gas of identical molecules which exchange energy upon colliding but otherwise are independent of each other.
		With this extension, the Boltzmann distribution is extremely useful in investigating the equilibrium behaviour of a wide range of both classical and quantum systems [a1], [a2], [a3].
		The Boltzmann weight is assigned to each unit face (plaquette) depending on the state variable configuration round the face.
	eom.springer.de /B/b120360.htm (705 words)

	Ludwig Boltzmann - FREE Ludwig Boltzmann Biography \| Encyclopedia.com: Facts, Pictures, Information!
		Boltzmann made important contributions to the kinetic theory of gases and to statistical mechanics—the Boltzmann constant, which relates the mean total energy of a molecule to its absolute temperature, is used widely in statistics and is named for him.
		In class, Vincenti had derived the famous Boltzmann relation, S = k log W which relates the entropy, S, of a gas to the Boltzmann constant, k, and W, the number of possible microstates...
		The Viennese physicist Ludwig Boltzmann was driven insane by the equation...
	www.encyclopedia.com /doc/1E1-Boltzman.html (1151 words)

	Vacuum History & Technology
		The Boltzmann constant, k, is a fundamental constant of physics occuring in nearly every statistical formulation of both classical and quantum physics.
		Boltzmann was also one of the first Europeans to recognize the importance of the electromagnetic theory proposed by James Clerk Maxwell of England.
		This empirical relation, formulated by Boyle in 1662, states that the pressure (p) of a gas varies inversely as its volume (v) at constant temperature; in equation form, pv=k, and is a constant.
	www.mcallister.com /vacuum.html (2681 words)

	Ludwig Boltzmann, pioneer in statistical physics (Site not responding. Last check: )
		Boltzmann was the first person to set up a viable theory of non-equilibrium thermodynamics.
		But this is useless, since the relation between V, T and P given by the equation of state holds only at equilibrium, and we do not know what relation we are to use if we are not in equilibrium.
		In Boltzmann's theory, the state is given by a very large number of variables, and the equation of motion was also given.
	www.mth.kcl.ac.uk /~streater/boltzmann.html (204 words)

	time per unit area, and is denoted M(T) (Site not responding. Last check: )
		Now the next step is to relate the energy in the cavity volume, (8), to the power per area per unit wavelength radiated from the surfaces of the walls of the cavity.
		This relation states that the power radiated (by an object) per area per unit wavelength is proportional to the fourth power of the temperature of that object.
		The resistance is geometrically related to the resistivity.
	godel.ph.utexas.edu /Students/rcrane/quantum/Blackbody/bb_home.htm (8175 words)

	History and outlook of statistical physics :: Statistical Mechanics
		In his paper of 1877 entitled "On the relation between the second law of the me chanical theory of heat and the probability calculus with respect to the theorems on thermal equilibrium", Boltzmann now presented a probabilistic expression for the en tropy.
		This relation has been called Boltzmann's Principle by Albert Einstein (1879-1955) in 1905 since it can be used as the foundation of statistical mechanics.
		He had realized that the pa pers of Maxwell and Boltzmann initiated a new discipline which could be applied to bodies of arbitrary complexity moving according to the laws of mechanics which were investigated statistically.
	statisticfunction.net /mech/index.html (1044 words)

	Boltzmann’s Anthropic Brain \| Cosmic Variance
		Boltzmann suggested that the entropy was really counting the number of ways we could arrange the components of a system (atoms or whatever) so that it really didn’t matter.
		On the one hand, Boltzmann’s fluctuations of entropy around equilibrium allow for the existence of dynamical regions, where the entropy is (just by chance) in the midst of evolving to or from a low-entropy minimum.
		Boltzmann’s goal is perfectly reasonable: to describe a history of the universe on ultra-large scales that is on the one hand perfectly natural and not finely-tuned, and on the other features patches that look just like what we see.
	cosmicvariance.com /2006/08/01/boltzmanns-anthropic-brain (13091 words)

	Thermodynamics, Temperature, Heat, Entropy - Numericana
		That relation comes from the fact that the mechanical work done by a force is the (scalar) product of that force by its displacement (i.e., the infinitesimal motion of the point which yields to it).
		A statistical definition of entropy (Boltzmann's relation) was first given by Ludwig Boltzmann (1844-1906) in 1877, using the constant k now named after him.
		Boltzmann's constant k = R/N is the ratio of the ideal gas constant (R) to Avogadro's number (N).
	home.att.net /~numericana/answer/heat.htm (6343 words)

	ICMP 2003: Plenary lectures
		This relation does not involve any details of the dynamics, and is in a strong sense purely kinematical.
		Analysis of the simplified models of advection has allowed to relate the transport properties of flows to nonstandard behaviors of fluid particles that is made possible by the lack of regularity of turbulent velocities.
		Most importantly, novel duality relations which involve open strings attached to branes on one side and various closed string backgrounds on the other, have blurred the traditional distinction between gauge- and string theory.
	icmp2003.net /lectures (2108 words)

	Plasma (physics) Encyclopedia Articles @ LaunchBase.org (Launch Base) (Site not responding. Last check: )
		While electric fields in plasmas are usually small due to the high conductivity, the electric field associated with a plasma moving in a magnetic field is not affected by Debye shielding.
		It is distinct from the three lower-energy phases of matter; solid, liquid, and gas, although it is closely related to the gas phase in that it also has no definite form or volume.
		For many purposes the electric field in a plasma may be treated as zero, although when current flows the voltage drop, though small, is finite, and density gradients are usually associated with an electric field according to the Boltzmann relation.
	www.launchbase.org /encyclopedia/Plasma_(physics) (3015 words)

	BOOK REVIEW
		Chapter 9 is entitles "Boltzmann's contributions to other branches of physics." I have previously mentioned (endnote 5)his studies in radiation theory leading to the famous Stefan-Boltzmann law.
		One thing not mentioned so far is the fact that Boltzmann's work eventually led recalcitrant scientists to accept the existence of atoms (although the final nail was not hammered into the coffin until Einstein's 1905 paper on Brownian motion).
		Chapter 11 "Boltzmann and his contemporaries" goes into some of the differing points of views which Boltzmann and his contemporaries shared, not only on the question of atoms but, more fascinatingly, on the whole problem of whether or not classical mechanics had any validity.
	www.pzweifel.com /music/boltzmann_secondo.htm (1549 words)

	Electrostatic ion cyclotron wave - Wikipedia, the free encyclopedia
		The angle (in radians) between the direction of propagation and the direction perpendicular to the magnetic field must be greater than about the square root of the mass ratio,
		in order that the electrons can move along the field lines from crest to trough to satisfy the Boltzmann relation.
		This relation is the result of restoring forces due to the Lorentz force (see Upper hybrid oscillation for more details), the electrostatic force (the T
	en.wikipedia.org /wiki/Electrostatic_ion_cyclotron_wave (143 words)

	MECH4470 Hypersonics and Rarefied Gas Dynamics
		According to Boltzmann's H -theorem its value of H, evaluated from the distribution function, is less than it was previously.
		Therefore Boltzmann's H -theorem cannot be true, if it purports to show that H will always decrease, as a result of collisions, starting from any initial conditions.
		Note that the initial conditions of the second gas had to be exactly specified to violate the H -theorem; a particular microstate of the gas was required as the initial condition.
	www.mech.uq.edu.au /~michael/m4470/s.htm (1656 words)

	British Journal of Pharmacology - Selective block of late Na+ current by local anaesthetics in rat large sensory ...
		The properties of the Boltzmann curve (Figure 2c), drawn according to best-fit parameters through derived permeability values, are similar to those previously published for activation of late Na current isolated by other means (Baker and Bostock, 1997) and this suggests that block does not exhibit substantial voltage-dependence.
		Rather, it reduced the slope of the relation, suggesting that drug binding does not promote inactivation of late current, and may slightly retard it (Figure 2e).
		The data presented were derived from TTX-sensitive records, and are compared with a Boltzmann relation previously presented as a best-fit to control channel availability data (Baker and Bostock, 1998a).
	www.nature.com /bjp/journal/v129/n8/full/0703261a.html (6260 words)

	Ceramide, a putative second messenger for nerve growth factor, modulates the TTX-resistant Na+ current and delayed ...
		The conductance-voltage relation is illustrated in the right panel of C where the data points have been fitted by the Boltzmann relation.
		The conductance-voltage relation is illustrated in the right panel; the data points have been fitted by the Boltzmann relation and are shown as the continuous lines.
		The effects of ceramide on the current- voltage relation obtained in embryonic capsaicin-sensitive sensory neurons are summarized in Fig.
	jp.physoc.org /cgi/content/full/544/2/385 (10060 words)

	Chapter 14. Boltzmann's Constant
		Therefore, in SE units, the value of Boltzmann's constant is an electron's rest-mass energy divided by its threshold temperature for a value of unity.
		The value of Boltzmann's constant in SG units is the same as it is in SE units because both the masson's rest-mass energy and threshold temperature are greater than those of the electron by the same factor
		Boltzmann's constant, Avogadro's number, and the universal gas constant do not exist, as such.
	www.writword.com /unituniv/c14.htm (248 words)

	The Frozen Texan: The Sklar-Eddington Objection to the Boltzmann Thesis
		According to Boltzmann’s final formulation of Statistical Mechanics, for any physical system chosen completely at random, there is a very high probability that the system will be very near or at equilibrium and a very low probability that it will be very far from equilibrium.
		So Boltzmann is faced with a problem: if that’s right, then the situation we actually find ourselves in is incredibly improbable: we are in a (part of the) universe that is quite far from equilibrium.
		In its essence, the Sklar-Eddington objection the Boltzmann thesis is the same as Kripke’s objection to monism: It seems possible for entropy to increase in the past direction of time and there is no explaining away this seeming because there is no distinct relation by which we identify entropy increase or the future.
	frozentexan.typepad.com /frozentexan/2005/08/the_sklaredding.html (4270 words)

	Plasma (physics) - WebArticles.com
		The ion density is related to this by the average charge stateÂ of the ions through.
		Differentiating this relation provides a means to calculate the electric field from the density:.
		It is distinct from the three lower-energy phases of matter; solid, liquid, and gas, although it is closely related to the gas phase in that it also has no definite form or volume.
	www.webarticles.com /print.php?id=390 (2030 words)

	[No title]
		The scale length of the presheath is set by either the mean free path for ions, or the scale length of the plasma, whichever is shorter [2].
		The distribution of ion energies for ions born with zero energy is known to be very sharply peaked as the ions enter the sheath [6].
		The mach number is related to the current density for ions entering the sheath.
	dusty.physics.uiowa.edu /~goree/papers/analytic_sheath.html (2931 words)

	[No title]
		It is shown that contrary to what is thought at present in this proportion the energy appearing in the Boltzmann factor is not a variable but it is a constant and the variable is the state accessible for the system having this constant energy.
		In other words the factor which at present is being used under the name of Boltzmann factor, because of using of some quantities other than what must be used in it, is a wrong factor.
		This means, according to the definition of temperature, that the condition of maximization of P(E) is that T and T', which are in turn the temperatures of the systems A and A', to become equal to each other.
	www.geocities.com /hvansari/11.txt (3883 words)

	[No title]
		Long before the transcendent role of entropy as a functional of probability theory was uncovered, Boltzmann's wrestling with the development of statistical mechanics led him to a result containing the answer.
		He claims that the Boltzmann entropy (3-1) is defined for each microscopic state and implies that the entropy is in fact a function of microsopic states, so that it evolves in time.
		If one takes seriously Boltzmann's relation (3-1) relating these multiplicities to Clausius' entropy, then it appears that the content of the Second Law of thermodynamics is already contained in classical mechanics.
	w3.uwyo.edu /~wtg/Issues/Issues3.html (4102 words)

	One from my many attempts to publish the controversial subject revived by the scanner (Site not responding. Last check: )
		It was generally accepted that Boltzmann had never given an exact proof of his H theorem (2), and so, when Shannon 40 years ago published his theory of communication (3) which introduced function H
		The weaker form is that (1) is a statistical form of thermodynamical entropy S. This was proofed by practice but Boltzmann‘s explanation of the relation of H and S was not understood, because Boltzmann himself did not take it seriously.
		Boltzmann connected entropy S with the logarithmic measure of the volume of partition orbits which for n going to infinity is approximated by (1).
	www.mujweb.cz /veda/kunzmilan/ent1.htm (3020 words)

	Thierry Goudon
		On Boltzmann equations and Fokker-Planck asymptotics : influence of grazing collisions, J.
		On fluid limit for the semiconductors Boltzmann equation, with A. (Toulouse) J.
		Homogenization and diffusion asymptotics for the linear Boltzmann equation, with A. MELLET (Toulouse), ESAIM-COCV, 9, 371-398, 2003.
	math.univ-lille1.fr /~goudon (1108 words)

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