
	Where results make sense

Topic: Statistical ensemble

Related Topics

Grand canonical ensemble

Canonical ensemble

Microcanonical ensemble

Density matrix

Statistical mechanics

Phase space

Derivation of the partition function

Entropy

Free energy

Second law of thermodynamics

First law of thermodynamics

Derivative

Helmholtz free energy

Chemical potential

Arrow of time

In the News (Sun 29 Nov 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Statistical ensemble (mathematical physics) - Wikipedia, the free encyclopedia
		Willard Gibbs in 1878, an ensemble (also statistical ensemble or thermodynamic ensemble) is an idealization consisting of a large number of mental copies (possibly infinitely many) of a system, considered all at once, each of which represents a possible state that the real system might be in.
		When the ensemble has an infinite number of members, it can be seen as defining a probability measure on the state space (phase space) of the system.
		The notional size of the mental ensembles in thermodynamics, statistical mechanics and quantum statistical mechanics can be very large indeed, to include every possible microscopic state the system could be in, consistent with its observed macroscopic properties.
	en.wikipedia.org /wiki/Statistical_ensemble (1144 words)

	Improved Probability Forecasting of Weather
		The statistical techniques are used to select the predictors from any available source, such as observations, numerical analyses and predictions, as well as other potential predictors (e.g., subjective forecasts of meteorological variables, road conditions or other weather-related variables), and to determine the optimal weights to assign to each predictor.
		Our statistical ensemble methodology can be tailored to the prediction of any and all weather-related variables, including precipitation type and amount, maximum and minimum temperatures, ceiling and visibility, fog, road-surface conditions, and sea-surface conditions, to mention a few.
		The mean probability predicted by the statistical/dynamical ensemble when the event occurred was significantly higher, and the mean probability predicted by the ensemble when the event did not occur was significantly lower, than that predicted by the other methods.
	www.gfdi.fsu.edu /~pfeffer/improvfinal.html (3495 words)

	Ensemble average
		The ensemble average of both of these intensities is simply the sum of the relevantensemble average intensities for the constituent components:...
		From a conceptual point of view, perhaps an ensemble average is the most...By averages we shall normally mean the ensemble average and denote it by an...
		This ensemble is useful for comparisons of the ensemble averages with...
	www.farmrestaurant.com /ensemble+average.html (896 words)

	Category:Statistical mechanics - Wikipedia, the free encyclopedia
		Statistical mechanics is the application of statistics, which includes mathematical tools for dealing with large populations, to the field of Mechanics, which is concerned with the motion of particles or objects when subjected to a force.
		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 every day life, therefore explaining thermodynamics as a natural result of statistics and mechanics (classical and quantum).
		In particular, it can be used to calculate the thermodynamic properties of bulk materials from the spectroscopic data of individual molecules.
	en.wikipedia.org /wiki/Category:Statistical_mechanics (146 words)

	Statistical ensemble -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-07)
		In (The science of matter and energy and their interactions) physics, a statistical ensemble is a very large set of similar systems, considered all at once.
		Putting aside for the moment the question of how statistical ensembles are generated (Click link for more info and facts about operationally) operationally, we should be able to perform the following two operations on ensembles A, B of the same system:
		In quantum physics, a general (A representative form or pattern) model for this convex set is the set of (Click link for more info and facts about density operators) density operators on a (A metric space that is linear and complete and (usually) infinite-dimensional) Hilbert space.
	www.absoluteastronomy.com /encyclopedia/s/st/statistical_ensemble.htm (613 words)

	ASU PHY 541: Thermodynamic Ensembles
		Thermodynamics and statistical mechanics are to approches to systems of large numbers of particles, such as solids or fluids.
		Thermodynamics is an empirical theory, and statistical mechanics is the underlying microscopic justification for thermodynamics.
		Statistical mechanics is the microscopic justification of thermodynamics.
	phy.asu.edu /phy541-shumway/ensembles.html (338 words)

	History and outlook of statistical physics :: Statistical Mechanics (Site not responding. Last check: 2007-11-07)
		The appearance of so-called statistical fluctuations in small subsystems was predicted by Boltzmann and he recognized Brownian motion as such a phenomenon.
		The term Statistical Mechanics has actually been coined by the great American physicist J. Willard Gibbs (1839-1903) at a meeting of the American Association for the Advancement of Science in Philadelphia in 1884.
		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 (1013 words)

	PARTITION FUNCTION (STATISTICAL MECHANICS) FACTS AND INFORMATION
		In statistical_mechanics, the partition function ''Z'' is an important quantity that encodes the statistical properties of a system in thermodynamic_equilibrium.
		It is a function of temperature and other parameters, such as the volume enclosing a gas.
		In ''classical'' statistical mechanics, it is not really correct to express the partition function as a sum of discrete terms, as we have done.
	www.witwik.com /Partition_function_(statistical_mechanics) (1641 words)

	Quantum Mechanics - Ensemble Interpretation (Site not responding. Last check: 2007-11-07)
		The Quantum Mechanical Ensemble Interpretation may be regarded as the simplest interpretation and might better be taken as the "correct" interpretation, until any new information that contradicts such an interpretation is made available.
		The Ensemble Interpretation does not attempt any explanation as to why Quantum Mechanics is the way it is. It simply states the most rational way of interpreting and calculating the results without introducing the contradictions that are inherent in the simple Copenhagen interpretation.
		The statistical distributions of the results are shown as histograms, and the root mean square half-widths or the two distributions deltaQ and deltaP, are indicated in fig.
	www.anasoft.co.uk /quantummechanics (2148 words)

	set.htm (Site not responding. Last check: 2007-11-07)
		Besides, if one of dynamic variables of the statistical ensemble can be considered as a probability density, the statistical ensemble can be used as a tool for a calculation of average values of physical quantities.
		In other words, a statistical description of stochastic systems is carried out on the base of dynamic properties of the statistical ensemble (considered as a dynamic system).
		The second property of the statistical ensemble is used rather slightly, or is not used at all.
	pavel.physics.sunysb.edu /~rylov/set.htm (431 words)

	Partition function (statistical mechanics) - Open Encyclopedia (Site not responding. Last check: 2007-11-07)
		In statistical mechanics, the partition function Z is an important quantity that encodes the statistical properties of a system in thermodynamic equilibrium.
		Most of the thermodynamic variables of the system, such as the total energy, free energy, entropy, and pressure, can be expressed in terms of the partition function or its derivatives.
		There are actually several different types of partition function, each corresponding to different types of statistical ensemble (or, equivalently, different types of free energy.) The canonical partition function applies to a canonical ensemble, in which the system is allowed to exchange heat with the environment at fixed temperature, volume, and number of particles.
	open-encyclopedia.com /Partition_function_(statistical_mechanics) (1270 words)

	Pitkanen III. (Site not responding. Last check: 2007-11-07)
		Self corresponds to the macrotemporal aspects of conscious experience and statistical ensemble aspect is crucial in the theory of consciousness.
		The notion of self means possible fundamental identification of two kinds of ensembles: the subjecto-temporal ensemble defined by the quantum jumps occurred after the last 'wake-up' and spatial ensembles defined by the subselves of self defining mental images of self as statistical averages over experiences of subselves of subselves.
		There are actually two statistical ensembles: the first one being associated with the final states of quantum jump and the second one being associated with the values of zero modes resulting in quantum jump.
	www.emergentmind.org /pitkanen_II.htm (5173 words)

	[No title]
		It is linear: the sum of two classical statistical statistical ensembles evolves into the sum of the two evolved ensembles.
		This linearity property is a trivial consequence of the fact that the elements of the ensembles are imaginary copies of one single physical system, in different contemplated states, and hence they do not interact with one another.
		Thus in classical statistical mechanics we have both the (generally) nonlinear equations for coupled {\it fields}, and also the (always) linear equation for a certain statistical quantity.
	www-physics.lbl.gov /~stapp/40369.txt (1874 words)

	Cellular Automaton Fluids: Basic Theory (1986)
		Such a description will typically be a statistical one, specifying not, for example, the exact configuration of particles, but merely the probabilities with which different configurations appear.
		This is the case for an ensemble in which all possible configurations occur with equal probability.
		Statistical results may nevertheless be applicable if the behavior of this single configuration is in some sense ``typical'' of the ensemble.
	www.stephenwolfram.com /publications/articles/ca/86-fluids/3/text.html (3013 words)

	L
		The statistical interpretation was rather popular in the USSR: The young physicist K.V.Nikol’skii rose with such an interpretation against his supervisor V.A.Fock, whose interpretation was very close to the Copenhagen one, the prominent specialist in radiophysics and optics L.I.Mandelstam presented a statistical interpretation in his authoritative lectures delivered at Moscow State University.
		Margenau, who developed his ensemble interpretation on the level of the minimal instrumentalist interpretation and abandoned the ensemble of particles as a theoretical concept (see sections 2 and 3), rejected the very notion of the reduction of the wave packet.
		In fact, they justified their ensemble approach on an operationalist basis: since quantum mechanics was a statistical theory, it should refer to a set of elements that is an ensemble of repeatable experiments.
	www.ihst.ru /personal/apech/stat.php (13352 words)

	Statistical Physics Using Mathematica
		The present courseware for statistical physics assumes that the reader is already familiar with Mathematica, but we also offer a course entitled Essential Mathematica for Students of Science that teaches the fundamentals of Mathematica using a tutorial approach that is suitable for self study; the getting started notebook provides sufficient background for this course.
		The basic postulates of statistical mechanics are used to derive and explain the laws of thermodynamics.
		The occupation representation is used to study the statistical mechanics and thermodynamics of ideal quantum gases satisfying Fermi-Dirac or Bose-Einstein statistics.
	www.physics.umd.edu /courses/CourseWare/StatisticalPhysics (1478 words)

	Project description after the Kick-off Meeting
		The output frequency of the predictability generated by SEPT must be at least 3 hourly although it is poor resolution of the reduced predictability that follows fronts.
		If we assume that the future lies in trading of certificates and it is the fl suppliers responsibility to buy enough of these, then the end-user might be a such a supplier, that doesn't know any details of the turbines and their location when the certificate is purchased.
		These are dependent on very long-term statistics, such that it will not be beneficial to change the statistical properties of the model system once the system is running in real time (see section on PCAT).
	www.ucc.ie /research/hmp/honeymoon/memorandum.html (5007 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		Such systems share peculiar properties, as for instance possible statistical ensemble inequivalence (negative specific heat), or very slow relaxations toward the equilibrium state.
		In a second part of the talk, we will propose a classification of situations of statistical ensemble inequivalence and of phase transitions, for systems with long range interaction.
		For many of these systems, large deviation techniques allow to prove that microcanonical statistical equilibrium is described by the maximization of an entropy with an energy constraint, whereas the canonical one is described by the associated free energy minimization.
	www.cpt.univ-mrs.fr /themes/groupe3/20030409.html (438 words)

	type_Document_Title_here
		(ii) application of a statistical ensemble technique, describing influence of the stochasticity upon a mean motion of particles.
		A statistical description of stochastic world lines needs a development of a special way of the statistical description appropriate for a description of stochastic lines.
		The statistical ensemble carries out a statistical description of the stochastic system independently of whether or not anyone of dynamic variables of the statistical ensemble can be regarded as a probability density.
	pavel.physics.sunysb.edu /~rylov/review.htm (919 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		STATISTICAL PHYSICS An Introductory Course by Daniel J Amit (Universita di Roma "La Sapienza" & The Hebrew University) & Yosef Verbin (The Open University of Israel) Preface (47k)
		Chapter 2.1: Historical background (446k) This invaluable textbook is an introduction to statistical physics that has been written primarily for self-study.
		It provides a comprehensive approach to the main ideas of statistical physics at the level of an introductory course, starting from the kinetic theory of gases and proceeding all the way to Bose—Einstein and Fermi—Dirac statistics.
	www.worldscibooks.com /physics/3526.txt (239 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		An ensemble is a collection of all microstates of a system, consistent with the constraints with which we characterize a system macroscopically.
		The probabilities of microstates in the corresponding ensembles can be derived in a way completely analogous to the derivation for the canonical ensemble, involving a subsystem and bath of constant temperature.
		Fluctuation formulas in the grand canonical ensemble are analyzed in the same fashion as in the canonical ensemble.
	kea.princeton.edu /ChE503/stat1.htm (1617 words)

	Statistical Modeling, Causal Inference, and Social Science
		Social Science Statistics is an excellent blog that is maintained by students of Gary King, Don Rubin, and others connected to the Government and Statistics departments at Harvard.
		I briey discuss the four relatively distinct statistical topics that were the primary focus of my work, all of which have been central to my published academic research for over three decades: missing data; causal inference; adjustment for covariates in observational studies; and meta-analysis.
		The standard in applied statistics seems much lower: what's expected is that we do one good data analysis, along with explorations of what might have happened had the data been analyzed differently, assessment of the importance of assumptions, and so on.
	www.stat.columbia.edu /~cook/movabletype/mlm (10297 words)

	Microscopic thermodynamics
		In fact, a rich statistical thermodynamics may be constructed from density functional theory.
		This is the grand canonical ensemble with the grand-canonical density matrix
		It may be noted that we have assumed the existence of a reservoir with which the system is free to exchange particles.
	www.cchem.berkeley.edu /~mhggrp/garnet/density/node13.html (488 words)

	Dr. Eli Altus (Site not responding. Last check: 2007-11-07)
		In the first, the recursive type equations have been transformed into a continuous form, leading to a nonlinear second order differential equation of damage evolution, for which an analytical solution is possible in some cases.
		Two major results have been obtained analytically: a) A relation between the ensemble statistical strength distribution and the commonly observed fatigue power law, and b) A relation between the scale of micro-failure probability of neighbor elements and the macro endurance limit phenomenon, without any a priori condition.
		The relation between damage morphology, statistical parameters and endurance limit, as proposed by the model will be briefly discussed.
	www.me.gatech.edu /me/events/seminars/Altus2.html (294 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		Vladimir Khristinich, Modeling a Two--Phase Liquid Flow and a Statistical Ensemble of Discrete Particles in a Collapsing Cavity In St. Petersburg University Mechanics Bulletin.
		We consider two phases: a liquid continuous medium and an ensemble of solid particles where the methods of continuous media are inapplicable and a statistical approach based on the kinatic theory of gases and liquids is necessary.
		We formulate the problem of statistical modeling of a particle flow in a liquid and derive equations which describe a continuous medium in a presence of a statistical flow of solid particles.
	www.math.spbu.ru /user/christ/cavity.htm (105 words)

	Statistical Mechanics of Cellular Automata (1983)
		The fractal dimensionality of the Cantor set is given by the negative of the entropy discussed below, associated with the ensemble of cellular automaton configurations (and hence real-number binary digit sequences) (Farmer, 1982a, 1982b).
		The entropy may equivalently be considered as the average number of binary bits necessary to specify one state in an ensemble of possible states.
		Representability of one cellular automaton by another under a simple encoding implies similar statistical properties for the two cellular automata, and forms potentially the basis for universality in statistical properties of cellular automata.
	stephenwolfram.com /publications/articles/ca/83-statistical/5/text.html (5319 words)

Try your search on: Qwika (all wikis)