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	Ideal chain - Wikipedia, the free encyclopedia
		The relevancy of the model is however limited, even at the macroscopic scale, by the fact that it does not consider any excluded volume for monomers (or, to speak in chemical terms, that it neglects steric effects).
		The most general answer is that the effect of thermal fluctuations tends to bring a thermodynamic system toward a macroscopic state that corresponds to a maximum in the number of microscopic states (or micro-states) that are compatible with this macroscopic state.
		Since the expression depends on the central limit theorem, it is only exact in the limit of polymers containing a large number of monomers (or thermodynamic limit).
	en.wikipedia.org /wiki/Ideal_chain (1673 words)

	Singular Behaviour of the Potts Model in the Thermodynamic Limit (Site not responding. Last check: 2007-10-31)
		The self--duality transformation is applied to the Fisher zeroes near the critical point in the thermodynamic limit in the q>4 state Potts model in two dimensions.
		A requirement that the locus of the duals of the zeroes be identical to the dual of the locus of zeroes (i) recovers the ratio of specific heat to internal energy discontinuity at criticality and the relationships between the discontinuities of higher cumulants and (ii) identifies duality with complex conjugation.
		This locus, together with the density of zeroes is shown to be sufficient to recover the singular form of all thermodynamic functions in the thermodynamic limit.
	www.maths.tcd.ie /report_series/abstracts/tcdm9801.html (146 words)

	Help.com - statistical mechanics (Site not responding. Last check: 2007-10-31)
		It provides a framework for relating the microscopic properties of individual atoms and molecules to the macroscopic or bulk properties of materials that can be observed in everyday life, therefore explaining thermodynamics as a natural result of statistics and mechanics (classical and quantum) at the microscopic level.
		However, Entropy in thermodynamics can only be known empirically, whereas in statistical mechanics, it is a function of the distribution of the system on its micro-states.
		In the thermodynamic limit, which is the limit of large systems, fluctuations become negligible, so that all these descriptions converge to the same description.
	help.com /wiki/Statistical_mechanics (2407 words)

	PPT Slide (Site not responding. Last check: 2007-10-31)
		thermodynamic potentials --> macroscopic parameters that are function of the measurable parameters, cannot be directly measured: ex.
		intensive parameters --> in thermodynamic equilibrium their value for the whole system is the same as the value for a part of the sytsem.
		extensive parameters --> in thermodynamic equilibrium their value for the whole system is the sum of the values for the parts.
	www.nd.edu /~zneda/mc/c1/tsld005.htm (320 words)

	Quantum Mathematics
		Quantum Theory and Its Stochastic Limit by Luigi Accardi, Igor Volovich, Yun Gang Lu (Springer Verlag) The subject of this book is a new mathematical technique, the stochastic limit developed for solving nonlinear problems in quantum theory involving systems with infinitely many degrees of freedom (typically quantum fields or gases in the thermodynamic limit).
		In the stochastic limit, the original Hamiltonian theory is approximated using a new Hamiltonian theory that is singular.
		The stochastic limit takes inspiration from the pioneering studies of quantum dynamical systems by Fermi, Bogoliubov, van Hove and Prigogine, and its main goal is a detailed qualitative study of quantum dynamics, in analogy to Poincare's qualitative study of classical dynamics.
	www.wordtrade.com /science/mathematics/quantummath.htm (2115 words)

	Helffer, Ramond: Semiclassical expansion for the thermodynamic limit of the ground state energy of Kac's operator
		Semiclassical expansion for the thermodynamic limit of the ground state energy of Kac's operator.
		We are interested here in the thermodynamical limit $\Lambda(h)$ of the ground state energy of this operator.
		Sjöstrand : Semiclassical expansions of the thermodynamic limit for a Schrödinger equation.
	www.numdam.org /numdam-bin/item?id=JEDP_2000____A13_0 (340 words)

	[No title] (Site not responding. Last check: 2007-10-31)
		In [10], the asymptotic expansion of the thermodynamic limit in powers of $h$ relies on a study of Laplace integrals in large dimension.
		The precise statement for applications to thermodynamic limit is given and proved in section 9.
		The two main problems are the existence of the thermodynamical limit $\Lambda (h)$, and the existence of its asymptotic expansion in powers of $h$ when $h\rightarrow 0$.
	www.ma.utexas.edu /mp_arc/papers/01-219 (5466 words)

	exchap08 (Site not responding. Last check: 2007-10-31)
		In the thermodynamic limit, show that we have the same expressions as calculated with periodic boundary conditions.
		Calculate the classical limit of the chemical potential of this gas.
		In the thermodynamic limit, the chemical potential of the three-dimensional gas is given by
	fge.if.usp.br /~ssalinas/exchap08 (517 words)

	CCFE - Center for Complex Fluid Engineering - Carnegie Mellon University
		Thermodynamic limit for polydisperse fluids by S. Banerjee, R.B. Griffiths and M. Widom, J. Stat.
		Thermodynamic limit for dipolar media by S. Banerjee, R.B. Griffiths and M. Widom, J. Stat.
		Repton model of gel electrophoresis in the long chain limit by M. Widom and I. Al-Lehyani, Physica A, 244 (1997) 510-521.
	cfe.cheme.cmu.edu /pubs_widom.htm (323 words)

	[No title] (Site not responding. Last check: 2007-10-31)
		The existence of this limit is not automatic; in fact one can without too much difficulties think of examples where the limit does not exist, due to possible coexistence of phases (equilibrium states) with different entropy densities, as happens for example in Potts models.
		Here we exclude this possibility by requiring the pressure (free energy density) function in the infinite-volume (thermodynamic) limit, which exists in great generality, to be differentiable as a function of (inverse) temperature.
		Note, however, that we do not need the local Gibbs states themselves to converge to a limit.
	www.ma.utexas.edu /mp_arc/html/papers/98-576 (1289 words)

	[No title] (Site not responding. Last check: 2007-10-31)
		In the case of a system in thermodynamic equilibrium the central role of W is, upon maximization, to distinguish between the high-probability manifold and that of low probability.
		As soon as one reaches the stage of calculating thermodynamic functions from a statistical mechanical model, however, passage to the limit is almost mandatory to render the calculation tractable.
		While recognizing the considerable importance of the IL to the mathematical study of the statistical mechanical model of thermodynamics, we are also aware of occasional over-interpretations of the tool that attribute to it an unwarranted physical significance.
	w3.uwyo.edu /~wtg/Issues/Issues8.html (3332 words)

	CiteULike: Thermodynamic limit of the first-order phase transition in the Kuramoto model (Site not responding. Last check: 2007-10-31)
		CiteULike: Thermodynamic limit of the first-order phase transition in the Kuramoto model
		Thermodynamic limit of the first-order phase transition in the Kuramoto model
		We analyze the convergence to the thermodynamic limit of two alternative schemes to set the natural frequencies.
	www.citeulike.org /user/nettraq/article/358740 (218 words)

	The high density, #tex2html_wrap_inline666# limit
		limit is the limit of maximum chemical potential, which is expected at high density.
		In this limit, the full problem, including the divergent terms, must be solved:
		Other thermodynamic quantities can be determined in a similar manner.
	www.nyu.edu /classes/tuckerman/stat.mech/lectures/lecture_20/node3.html (717 words)

	Piet Hut: Gravitational Thermodynamics
		A thermodynamic treatment of self-gravitating systems is fraught with peril: from a formal point of view, it cannot even be defined, because there is no thermodynamic limit.
		While intensive thermodynamic quantities like density and temperature stay constant under scaling, and extensive quantities such as energy and particle number grow linearly with mass, potential energy turns out to be a superextensive quantity, scaling like the five-thirds power of the mass.
		In practice, however, the deviations from a true thermodynamic equilibrium are often not that large, and N-body simulations show a relatively smooth behavior of the approximate thermodynamic parameters as a function of time.
	www.ids.ias.edu /~piet/act/phys/thermo (1167 words)

	Thermodynamic self-consistency: Configurational temperature
		24) methods to assess whether or not a trial pair potential describes a system's interactions in a thermodynamically self-consistent manner.
		Even though the different definitions have substantially different dependences on sample size, they all extrapolate to the thermodynamic temperature in the thermodynamic limit.
		The successful collapse of the configurational and hyperconfigurational temperatures to the thermodynamic temperature constitutes a set of stringent internal self-consistency tests for the accuracy of the measured pair potential and its correct interpretation.
	www.physics.nyu.edu /~dg86/codef04b/node5.html (967 words)

	Zero-temperature thermodynamics (Site not responding. Last check: 2007-10-31)
		In the thermodynamic limit, we may take the sum over to an integration:
		These are referred to as the zero-point energy and pressure and are purely quantum mechanical in nature.
		The fact that the pressure does not vanish at T=0 is again a consequence of the Pauli exclusion principle and the effective repulsive interaction that also showed up in the low density, high temperature limit.
	www.nyu.edu /classes/tuckerman/stat.mech/lectures/lecture_19/node4.html (215 words)

	Relating Single-Molecule Measurements to Thermodynamics -- Keller et al. 84 (2): 733 -- Biophysical Journal
		limits the applicability of the model to cases where the extension
		The closest single-molecule analogs of the thermodynamic free
		on the intensivity and extensivity of thermodynamic parameters.
	www.biophysj.org /cgi/content/full/84/2/733 (2962 words)

	ARC Centre of Excellence for Mathematics and Statistics of Complex Systems
		Two-dimensional thermodynamic-scaling allows detailed study of a substantial region of thermodynamic state space in a single Monte Carlo (MC) realisation; for example one can obtain essentially continuous data (on free energies as well as ensemble averages) over large regions of temperature and density (TDSMC) or of temperature and chemical potential (TMuSMC).
		A general problem of interpreting MC data is that for the small systems that are actually accessible the derived behaviour differs from that of a bulk system (i.e.
		from the so-called “thermodynamic limit”); in particular the size-dependent behaviour depends on the statistical ensemble employed (canonical, isothermal-isobaric, grand canonical, Gibbs), and alternative choices of thermodynamic definitions (even though these may be equivalent in the bulk limit) can lead to apparently discrepant behaviours.
	www.complex.org.au /conferences/MC2003/valleau.html (209 words)

	4.2 The thermodynamic limit of the spin chain
		This is necessary, as the classical string solutions only limit to the true quantum result in the BMN type limit
		This thermodynamic groundstate solution of the gauge theory Bethe equations was found in [22, 16, 8, 54], which we closely follow.
		The thermodynamic limit is now obtained by first taking the logarithm of (71
	relativity.livingreviews.org /Articles/lrr-2005-9/articlesu8.html (557 words)

	Thermodynamic limit and semi-intensive quantities
		The properties of statistical ensembles with Abelian charges close to the thermodynamic limit are discussed.
		A new class of variables (semi-intensive variables) which differ in the thermodynamic limit depending on how charge conservation is implemented in the system is introduced.
		The thermodynamic limit behaviour of these variables is calculated through the next-to-leading order finite volume corrections to the corresponding probability density distributions.
	stacks.iop.org /0954-3899/31/1421 (250 words)

	A short course in Eiffel (Site not responding. Last check: 2007-10-31)
		A requirement that the locus of the duals of the zeroes be identical to the dual of the locus of zeroes in the thermodynamic limit (i) recovers the ratio of specific heat to internal energy discontinuity at criticality and the relationships between the discontinuities of higher cumulants and (ii) identifies duality with complex conjugation.
		Conjecturing that all zeroes governing ferromagnetic singular behaviour satisfy the latter requirement gives the full locus of such Fisher zeroes to be a circle.
		This locus, together with the density of zeroes is then shown to be sufficient to recover the singular part of the thermodynamic functions in the thermodynamic limit.
	www.maths.tcd.ie /report_series/abstracts/tcdm9707.html (142 words)

	On the thermodynamic limit for Hartree-Fock type models - Catto, Le Bris, Lions (ResearchIndex) (Site not responding. Last check: 2007-10-31)
		Abstract: We continue here our study [10, 11, 13] of the thermodynamic limit for various models of Quantum Chemistry, this time focusing on the Hartree-Fock type models.
		For the reduced Hartree-Fock models, we prove the existence of the thermodynamic limit for the energy per unit volume.
		We also define a periodic problem associated to the Hartree-Fock model, and prove that it is well-posed.
	citeseer.ist.psu.edu /428467.html (961 words)

	AMCA: Quantum Effects in Mean Field Electron Dynamics by Alex Gottlieb (Site not responding. Last check: 2007-10-31)
		Vlasov's equation for plasmas can be derived from a model of quantum N-electron dynamics: one considers "jellium" electrons with a truncated Coulomb interaction and derives the classical Vlasov equation in the thermodynamic limit [1].
		Recent work indicates that the time-dependent Hartree equation (a weakly nonlinear Schroedinger equation) provides a kind of semiclassical correction to Vlasov's equation in the same thermodynamic limit [2].
		However, if there is some confinement of electrons at the nanoscale, as there is in semiconductor quantum wells, then quantum behavior must survive the limit N tends to infinity.
	at.yorku.ca /c/a/n/t/08.htm (260 words)

	[No title] (Site not responding. Last check: 2007-10-31)
		Lecture 3 : Phase transitions, first part (Thursday 6 Feb 2003) I Thermodynamic limit theorem for the entropy: Thermodynamic limit theorem: for suitable hamiltonians (i) the following limit exists if N has a terminating binary expansion (although it may be - infinity for some E,N,V, e.g.
		S= - dF/dT) III Phase transitions These occur when there is some singularity in the thermodynamic functions, for example when water boils, the density or volume depends discontinuously on the temperature at constant pressure (draw (P,T) diagram).
		Appendix : sketch of proof of the thermodynamic entropy theorem (to be added later)
	www.ma.hw.ac.uk /~oliver/lectures/3.txt (468 words)

	Relation Day 2003 - Abstracts (Site not responding. Last check: 2007-10-31)
		The literature of statistical physics relies heavily on the notions of the thermodynamic limit and of Gibbs state.
		I propose a general definition of the thermodynamic limit based on nonstandard analysis that encompasses both the standard theory and in addition mean field models like the Sherrington-Kirkpatrick mean field spin glass model.
		This model allows a very general definition of pure state, and hence of the notion of symmetry breaking in the thermodynamic limit.
	www.cosc.brocku.ca /~duentsch/abstracts.html (691 words)

	Quantum mechanics and thermodynamic limit (Site not responding. Last check: 2007-10-31)
		I have read some papers on arxiv: http://arxiv.org/abs/quant-ph/0403111 http://arxiv.org/abs/quant-ph/0402072 http://arxiv.org/abs/quant-ph/0402072 and I have not clear at all why thermodynamic limit should work here.
		I have learned from my undergraduate courses that an oscillating function has not limit in this case.
		Prev by thread: Re: When is V^2 the magnitude of V? Next by thread: Re: Quantum mechanics and thermodynamic limit
	www.lns.cornell.edu /spr/2004-03/msg0059474.html (68 words)

	Complexity Digest - Multi-information in the Thermodynamic Limit
		Multi-information in the Thermodynamic Limit, SFI Working Papers
		Abstract: A multivariate generalization of mutual information, multi-information, is defined in the thermodynamic limit.
		Source: Multi-information in the Thermodynamic Limit, Ionas Erb and Nihat Ay, DOI: SFI-WP 03-11-064, SFI Working Papers
	www.comdig.org /article.php?id_article=14314 (124 words)

	STATISTICAL MECHANICS (Site not responding. Last check: 2007-10-31)
		This classic book marks the beginning of an era of vigorous mathematical progress in equilibrium statistical mechanics.
		Its treatment of the infinite system limit has not been superseded, and the discussion of thermodynamic functions and states remains basic for more recent work.
		The conceptual foundation provided by the Rigorous Results remains invaluable for the study of the spectacular developments of statistical mechanics in the second half of the 20th century.
	www.worldscibooks.com /physics/4090.html (177 words)

	Optical design and fabrication : Concentrators
		Curved diffractive optical element for uniform concentration at the thermodynamic limit at finite distance
		Light collimation, imaging, and concentration at the thermodynamic limit
		Anamorphic Concentration of Solar Radiation Beyond the One-Dimensional Thermodynamic Limit
	www.opticsinfobase.org /ocisdirectory/220_1770.cfm (153 words)

	The Thermodynamic Limit (Site not responding. Last check: 2007-10-31)
		the number of particles per volume, and takes the limit for N,V tending to infinity.
		Of course the question of existence of these thermodynamical limits poses lots of mathematical problems; furthermore it would be convenient to replace the thermodynamic limit by working directly with systems defined on classical configuration spaces of infinite volume.
		One expects that since these systems tend to show continous spectra the DOS or at least the IDS should become relativly well behaved functions compared to the Dirac measure/stair function for the discrete spectra.
	www-user.tu-chemnitz.de /~mjg/Talks/BlochDOS/node11 (138 words)

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