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Topic: Microstate continuum

	Molecular and Cellular Biophysics - Cambridge University Press
		The microstates interconvert rapidly and the global state reflects the average behavior of these microstates.
		A collection of microstates forms an ensemble, and statistical mechanics provides the conceptual tools for understanding a global state in terms of its constituent microstates.
		Microstates of a protein can be further distinguished by different positions and orientations of the surrounding water molecules, and possibly by ions in solution.
	www.cambridge.org /us/catalogue/catalogue.asp?isbn=9780521624701&ss=exc (3300 words)

	Ludwig Boltzmann and Entropy - Resonance - September 2001
		This space is a continuum, so what we mean by the `number of states' is simply the volume (generalised to 6N dimensions) of phase space occupied by the gas molecules.
		Thus it becomes clear that entropy is intimately associated with the number of microstates for a given macrostate.
		Now remove the constraint and allow access to the whole volume V. The number of microstates is now (V/v)N, which is larger by a factor of 2N than that for the constrained case (and remember that N ~ 1023).
	www.ias.ac.in /resonance/Sept2001/Sept2001p3-5.html (1393 words)

	SNS: A Field Guide to Time
		Without knowledge of the particular microstate of the system, we assume it is equally likely to be in any of the microstates that correspond to the known macrostate.
		The only mathematically meaningful probability that can then be assigned to any particular microstate is precisely zero, which is rather blatantly at odds with the assumption that is in fact in some particular microstate.
		The persisting problem with this picture is that we have no reason, short of a statistical postulate, to believe that the system is not, in fact, on one of the few trajectories that correspond to the system staying in a low-entropy region or moving to a lower-entropy region.
	severinghaus.org /personal/writings/essays/a_field_guide_to_time.html (3833 words)

	Time Travel [Internet Encyclopedia of Philosophy]
		By the early to mid-twentieth century, time travel stories evolved to take into account the features of an Einsteinian universe: a four-dimensional spacetime continuum that curves and in which time has the character of a spatial dimension (that is, there can be local variations or "warps").
		Microstate and macrostate entanglement occurs when an observer measures some physical property, like spin, with some instrumentation.
		The rule, according to the orthodox (or Copenhagen) interpretation, is that when observed the state vector (the equation describing the entangled system) reduces or jumps from a state of superposition to one of the actually observed states.
	www.iep.utm.edu /t/timetrav.htm (7851 words)

	[No title]
		Given Ω microstates at a particular energy, the probability of finding the system in a particular microstate is p = 1/Ω.
		This postulate is necessary because it allows one to conclude that for a system at equilibrium, the thermodynamic state (macrostate) which could result from the largest number of microstates is also the most probable macrostate of the system.
		The probabilities of the various microstates must add to one, and the normalization factor in the denominator is the canonical partition function:
	www.algebra.com /~pavlovd/wiki/Statistical_mechanics (2349 words)

	What is Life?
		The biotic energy state (life) is the convergence of a set of available microstates, at a given moment, that operate limiting the increase of more microstates to which the energy could be spontaneously dispersed or diffused.
		However, a strict set of microstates determines a cell, or a multicellular being to be alive.
		The living thermodynamic systems maintain a cuasi-stable amount of microstates that had to be increased spontaneously (change of entropy), temporarily expanding the increase of their local entropy.
	www.biocab.org /Life.html (5415 words)

	No Title
		The Monte Carlo method is a way of generating states such that the probability of a state is given by the appropriate distribution for the chosen ensemble.
		The process of moving from one microstate to another is a stochastic process.
		Keep in mind that in nature there is a continuum between small crystallites with grain boundaries and a truly amorphous system with no preferred direction.
	phycomp.technion.ac.il /~phr76ja/theme/thefinal.html (2566 words)

	Local conformational fluctuations can modulate the coupling between proton binding and global structural transitions in ...
		the population distribution in the ensemble of microstates of
		Each microstate exhibits dual structural character and consists of a mixture of regions that are considered to be native-like (red) and regions that are treated thermodynamically as unfolded (yellow).
		microstates plotted as a function of the fraction native (number of residues in folded segments/total number of residues) at three different pH values (pH 7, 4, and 3).
	www.pnas.org /cgi/content/full/102/12/4282 (4132 words)

	Where does the Boltzmann factor come from?
		There are six ways to get a total of 7 from the "microstates" of the two dice, but only one way to get a total of 2 (snake-eyes) or 12 (boxcars), so 7 is more likely.
		If you have hundreds of fair dice and put them all together, the total for which the number of possible microstates is at a maximum is (if you work it out) at a value of 3.5 times the number of dice.
		This description is a little overidealized, because of course the oscillators won't all be at the same energy level to begin with, and they might not all be identical, so the spacing to the next level will in general vary.
	world.std.com /~mmcirvin/boltzmann.html (2622 words)

	Statistical mechanics - Wikipedia Mirror (Site not responding. Last check: 2007-10-30)
		This postulate is necessary because it allows one to conclude that for a system at equilibrium, the thermodynamic state (macrostate) which could result from the largest number of microstates is also the most probable macrostate of the system.
		The macroscopic state of maximal entropy for the system is the one in which all micro-states are equally likely to occur during the system's fluctuations.
		The probabilities of the various microstates must add to one, and the normalization factor in the denominator is the canonical partition function:
	www.wiki-mirror.be /index.php/Statistical_mechanics (2992 words)

	Sample Chapter for Haddad, W.M., Chellaboina, V., Nersesov, S.G.: Thermodynamics: A Dynamical Systems Approach.
		He goes on to argue that Clausius' thermodynamic entropy (a macroscopic quantity) is proportional to the logarithm of the probability that a system will exist in the state it is in relative to all possible states it could be in.
		As a result of this approach, modern continuum thermodynamics was developed using theories from elastic materials, viscous materials, and materials with memory [30, 34, 35, 44].
		The main difference between classical thermodynamics and rational thermodynamics can be traced back to the fact that in rational thermodynamics the second law is not interpreted as a restriction on the transformations a system can undergo, but rather as a restriction on the system's constitutive equations.
	press.princeton.edu /chapters/s8122.html (5159 words)

	Einstein's Office: Discreteness versus Continuum (Site not responding. Last check: 2007-10-30)
		Another way of looking at it is by focusing on the impact of quantum mechanics on our classical notion of our physical world which assumes 'continuum' values in physical quantities such as energy (or spin etc) into having a 'discrete' or 'quanta' set of values.
		We have several theories all of which are proposed in order to resolve such issues, but essentially all of them face the obstacle of having to get over the same issue of incorporating these two concepts of 'discreteness' and 'continuity' together in a nice harmonic way.
		But the interesting question here is, whether the process of assigning continuum of probabilities reflect our lack of knowledge of the system due to energy fluctuation or that the nature inherently posesses this continuum property itself.
	precondition.blogspot.com /2006/08/discreteness-versus-continuum.html (727 words)

	Statistical mechanics - Gurupedia
		probability of a microstate of energy E is proportional to
		The probabilities of the various microstates must add to one, and the normalization factor is the partition function:
		The partition function is a measure of the number of states accessible to the system at a given temperature.
	www.gurupedia.com /s/st/statistical_mechanics.htm (916 words)

	Multi-Conformer Continuum Electrostatics (MCCE)
		As surface water and salt can be taken into account by the continuum model, these molecues are recursively stripped off if they are exposed with the SAS exceeding this cutoff threshold.
		The sampling starts from a totally random microstate which might be at "high" energy state, and gradually "cooled" down to equilibrated states.
		And in every MC step the occupied microstate is checked against all collected microstates to see if it is a new unique one.
	www.sci.ccny.cuny.edu /~mcce/doc/running_mcce3.php (2959 words)

	The Nature of Life*
		S has various "macro-level" states (macrostates) and various "micro-level" states (microstates); S's microstates are the states of its parts.
		Further, there is a relatively simple and implementable microdynamic, call it D, which governs the time evolution of S's microstates; in general, the microstate of a given part of the system at a given time is a result of the microstates of "nearby" parts of the system at preceding times.
		First, "external conditions" are conditions affecting the system's microstates that are extraneous to the system itself and its microdynamic.
	www.reed.edu /~mab/papers/life.OXFORD.html (10560 words)

	Simulation of the Electron Transfer between the Tetraheme Subunit and the Special Pair of the Photosynthetic Reaction ...
		The formalism is applied to the kinetics of electron transfer in the tetraheme subunit and the special pair of the reaction center of Blastochloris viridis.
		It is shown that continuum electrostatic calculations can be used in combination with an existing empirical rate law to obtain electron-transfer rate constants.
		The re-reduction kinetics of the photo-oxidized special pair simulated in a microstate formalism is shown to be in good agreement with experimental data.
	www.bisb.uni-bayreuth.de /People/ullmann/paper/Becker2007/abstract.html (218 words)

	Heat capacity: Encyclopedia of chemistry, analytics & pharmaceutics with 64,564 entries.
		The reason is that gases with very large molecules, in theory have almost the same high-temperature heat capacity as solids, lacking only the (small) heat capacity contibution that comes from potential energy that cannot be stored between separate molecules in a gas.
		The Dulong-Petit "limit" results from the equipartition theorem, and as such is only valid in the classical limit of a microstate continuum, which is a high temperature limit.
		For light and non-metallic elements, as well as most of the common molecular solids based on carbon compounds at standard ambient temperature, quantum effects may also play an important role, as they do in multi-atomic gases.
	www.chemie.de /lexikon/e/Heat_capacity (2703 words)

	R. N. ELLIOTT ON SOCIAL MOOD...
		As a result of this work, it was shown that macro-states could be used to describe a complex system and that these could be accounted for in terms of macro-variables that did not make reference to the atomistic constituents of the complex system.
		Indeed, any given macro-state is compatible with many different microstates and thus is not uniquely determined by a single microstate.
		Thus, the properties of wholes could be studied in and of themselves since they have properties of their own that were not merely the sum of their constituents.
	www.mi.sanu.ac.yu /vismath/proceedings/green.htm (1982 words)

	Amazon.com: "distinct microstates": Key Phrase page (Site not responding. Last check: 2007-10-30)
		Thus for the macroscopic observer to confuse distinct microstates, the product AxAp must be larger than its minimum value-an observation of the system provides measurements of the position and...
		For this gas, interchange of molecules does not correspond to distinct microstates because the molecules are indistinguishable.
		this state is the most probable because there are the most possible ways to produce it, the greatest number of distinct microstates all of which have the same macroscopic consequences.
	www.amazon.com /phrase/distinct-microstates (415 words)

	School of Theoretical Physics - Seminars
		In terms of the proposal, a bound for the entropy contained in this region can be derived from a counting of potential ``degrees of freedom'' associated to the Cauchy horizon of its future domain of dependence.
		For different spherically symmetric spacelike regions in Minkowski spacetime of arbitrary dimension, we show that this proposal leads, in the continuum approximation, to Susskind's well-known spherical entropy bound.
		I will try to describe some of the experimental evidence that leads us to believe that the fireball produced in Au-Au colissions at RHIC is a rapidly thermalizing, strongly-coupled Quark-Gluon-Plasma (sQGP).
	www.stp.dias.ie /TPPG/seminars.shtml (1559 words)

	Boltzmann's Work in Statistical Physics (Stanford Encyclopedia of Philosophy)
		That probability distribution was now determined by the size of the volume in phase space corresponding to all the microstates giving rise to the same macrostate, (essentially given by calculating all permutations of the particles in a given macrostate).
		Thus, the correct statement that, in the case that √(a/b) is irrational, the trajectory will traverse, for each value of x, an infinity of values of y within any interval however small, could easily have lead him to believe (incorrectly) that all values of x and y are traversed in the course of time.
		The relation between macro- and microstate is obviously non-unique since many different microstates, e.g., obtained by permuting the molecules, lead to the same macrostate.
	plato.stanford.edu /entries/statphys-Boltzmann (12986 words)

	Peder Voetmann Christiansens homepage
		There is nothing wrong with Shannon's "Theory of Information" when we remember that the potential meaning of the Shannon-information is outside the scope of the theory and is left to the human listener on the telephone.
		Also, there is nothing wrong with the information theoretical description of physical entropy as potential information about the microstate of a physical system, so it is not just a funny coincidence that Shannon's information and Gibbs' entropy are given by the same probabilistic formula.
		The physical information theory, as worked out by Szilard and Brillouin (note 8) in the discussion of Maxwell's demon has something important to say on the physical limits of how much structure a system can exhibit, but it can say nothing about whether these structures are meaningful or not.
	mmf.ruc.dk /~PVC/emertext.htm (4163 words)

	[No title]
		In this approach, the entropy of a macrostate can be interpreted as the number of bits that would be required to specify the microstate of the system.
		(Of course, in classical statistical mechanics the phase space of states is a continuum, so that the number of bits needed to specify a microstate {\em completely} is infinite.
		This can be avoided in the usual way by specifying the microstate to a finite, and arbitrary, resolution in phase space.) In quantum systems, however, the expression for entropy (first proposed by von Neumann \cite{vonneumann}) is not identical to the Shannon entropy.
	www.ai.mit.edu /projects/im/ftp/poc/schumacher/qubit.tex (4283 words)

	portland imc - 2003.08.08 - Words to Seduce the Left
		They deny economic free-association (the fascistic microstate called the capitalist corporation is many things, but 'free' sure as hell ain't one of them) and personal liberty.
		Keep in mind, this isn't "biology" because who counts as "relatives" and who doesn't is a social contruct.
		So what we get (within Anarchism) is a continuum for "collectivism" with only the STRICT individualist anarchists being totally non-collectivist.
	portland.indymedia.org /en/2003/08/269504.shtml (1307 words)

	chap1.html
		Obviously that is just equal to the number of states of system 2.
		<~1 then the individual particles cannot be treated as a smooth continuum.
		It will be seen later that this means that collisions dominate the behaviour: i.e.
	silas.psfc.mit.edu /introplasma/chap1.html (1234 words)

	Improved pKa calculations through flexibility based sampling of a water-dominated interaction scheme -- Warwicker 13 ...
		Koumanov, A., Ruterjans, H., and Karshikoff, A. Continuum electrostatic analysis of irregular ionization and proton allocation in proteins.
		Warwicker, J. Continuum dielectric modelling of the protein–solvent system, and calculation of the long-range electrostatic field of the enzyme phosphoglycerate mutase.
		You, T.J. and Bashford, D. Conformation and hydrogen ion titration of proteins: A continuum model with conformational flexibility.
	protsci.highwire.org /cgi/content/full/13/10/2793 (5326 words)

	[No title]
		At any moment W is a measure of the phase volume of all those microstates compatible with the macroscopic constraints - and lnW is the maximum of the information entropy at that instant.
		A retardation problem might exist if we were trying to follow the system's changing occupation of microstates, but we are not, because we cannot.
		Although any complete theory of nonequilibrium must be a continuum field theory, we shall omit spatial dependence explicitly here in the interest of clarity and return to address that point later.
	w3.uwyo.edu /~wtg/entropy.html (6533 words)

	Is World Year of Physics ended ?
		Systems of course are continually transitioning between these microstates as the particles interact, but overall you won't notice this with a large-scale/coarse measurement like say pressure (which is the summation of alot of little hits against a surface).
		So if you have more microstates (higher W), then by the above definition S will be larger too, and of course more microstates contribute more to the numerator of any probability calculation (the denominator being some total state count - or a total ensemble count).
		Condensed matter resembles a continuum, and a fl hole analog is a Laval nozzle, where fluid flow changes from subsonic to supersonic (forming an event horizon for sound waves).
	einstein.phys.uwm.edu /forum_thread.php?id=3470 (9570 words)

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