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probability distribution on a set of microstates. Landau and
Lifschitz explicity warn against this error in their *Statistical Physics*. See page 18 of *Fundamental Principles of Statistical Physics*, 2nd ed. There seems to be a free on-line copy somewhere. There is also carelessness in the difference between a probability distribution on a (e.g.) discrete basis of microstates, and the (continuous) space they span.
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It must be emphasised that the averaging over various Ψ states, which we have used in order to illustrate the transition from a complete to an incomplete quantum-mechanical description, has only a very formal significance. In particular, it would be quite incorrect to suppose that the description by
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I think there is a problem associating it with minds, because that suggests that if minds didn't exist then neither would ensembles. I'm not trying to be picky or argue for argument's sake; I would prefer a formulation which is consistent with other similar abstractions in statistics or mathematics.
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You're absolutely right, a generic ensemble should not be thought of as a classical probability distribution over pure states. If the article gives that impression it should certainly be corrected. (The exception is the case of equilibrium ensembles, especially thermodynamic ensembles, where it is
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i've made some edits and supplied a few details. the intro of the article is still rather sloppy. Since there's "mathematical" in the title, that should be the context of the article. not some stuff on, say, meterology. surely that could be mentioned as a side remark, but that should not interrupt
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How about "virtual" or "possible"? I think "mental" is inappropriate here. It is not a "thought experiment", but a class of mathematical models. Nor are you holding those possible states of an ensemble in your mind. Finally, nobody actually uses the term "mental states". When I googled for "mental
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Trying to be "operational" is a little bit philosophical. Also a little biassed. But to point out that an alternative definition of the quantum statistical ensemble is as a mapping from observables to expectations is an excellent idea, and to mention that
Gleason's theorem or whatever shows the
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This article is badly written, full of slight grammatical errors that nevertheless produce unintelligiblity in a few crucial passages, and suffers from a serious physics error in the description of the quantum mixed state. Mixed state is a synonym for statistical ensemble, and in QM it is not a
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No. I think you're thinking about the practical running of an ensemble of climate models. But that's really only a derived use of the word -- fundamentally it's called an ensemble because it's supposed to be a collection of states (and dynamics) that we've dreamed up which we hope may be
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Having taught statistics at four universities, including one renowned throughout the world, I have not encountered the phrase "statistical ensemble" used in this sense. Certainly populations and samples are mentioned all the time, but when is this term ever used except by physicists?
928:"Imaginary" I don't like, because of the association with complex numbers. "Imagined" I could live with; but I think "mental" is better, because (IMO) it's simpler and more immediate. Is there a problem in the association with "mind"? -- That is where the ensemble lives.
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OK, you make a valid point, but I still prefer a better phrasing. I don't like the association with "minds"; how about "imaginary"? or "imagined". If you do not like these, please give this some thought and try to find another expresion. I will also think about better
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863:. But in 1878 Gibbs goes beyond this by considering the probability distribution for the system as a whole. There is now no longer a population of real subsystems: there is now only one real system, in one (unknown) state. But because it is useful to
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means of the density matrix signifies that the subsystem can be in various Ψ states with various probabilities and that the averaging is over these probabilities. Such a treatment would be in conflict with the basic principles of quantum mechanics.
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may not literally be a stub, but it doesn't stand alone very well. I'd support this merge and redirect; could make this content a subsection. Would also benefit after the merger from the addition of average formulas from other ensembles.
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Schroedinger uses the word "mental": p. 3, Statistical
Thermodynamics. The word is pretty standard. Standard usage should be respected in spite of one's own personal philosophical critiques. What word does Gibbs use, anyway?
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Since in the quantum mechanical case, ensembles are modeled by density operators, this is a cleaner approach to the pure-state mixed-state dichotomy, because equivalence classes of ensembles have the structure of a convex set.
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The new changes to the article regard a very unusual interpretation of statistical ensemble. I am reverting. If there is indeed a usage in meteorology which is different, then this should be place in another
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defined in the following sense: there is some laboratory procedure for producing systems which are instances of this ensemble. By repeating this laboratory procedure we obtain a sequence of systems
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According to the article's introduction, there are three possible titles for this article: "ensemble", "statistical ensemble" and "thermodynamic ensemble", with "ensemble" being the main one.
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states" and "ensembles", all I got (that was remotely relevant) was some articles talking about neurodynamics and a dissertation about the quantum mechanics of a conscious observer. --
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might be left out of the article, but here is an explanation: A sequential ensemble defines a state by the time average of measurements: e.g. for each quantum
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assumption, but for explaining the operational meaning of ensemble I think this is good enough. Using
Gleason's theorem this is given by a density operator
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the coherence and continuity of the mathematical presentation of the article, and that's what the non-mathematical remarks in the present version are doing.
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equivalence is very good, as well. Dragging in ergodicity seems a little otiose, even worse than dragging in measurements and operationalisablitiy....
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common and convenient to represent them by a probability distribution over energy eigenstates.) Anyhow, feel free to edit the article and
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Whatever else, it should be possible to access the usual classical statistical ensembles used by physicists and chemists, namely:-
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Would "similar" or "diversified" suffice? I don't think there is a requirement for the copies to be exact, just proprogated.
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IMO it is thus important that the word "mental" (or something very similar) should remain in the article to flag this point.
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ensemble; but only approximately correct at any one time, and subject to fluctuation, when we consider it as a fraction of a
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In fact there is a lot of complex stuff in this article which I think would be better placed in a referenced page for
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Why are there two links to the Korean version in the languages box? Does someone know how to edit this - I don't. --
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Why do we have the unnecessary disambiguation (the parenthetical "mathematical physics" at the end of the title -
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is a similar abstraction. Choosing terms carefully will have a payoff, I think. But I concede your larger point.--
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subsystems, each statistically independent. This is the idealization used by
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Also how about defining a grand ensemble as an ensemble of ensembles. Perhaps include a diagram such as at a)
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Could we use a different expression other than "mental". Isn't it enough to say it is an idealization? --
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in the real world. They are a thought-experiment, as one considers all the different states the system
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on 3 October 2022. For the contribution history and old versions of the redirected page, please see
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821:. There should be short definitions of the three here, too. This appears to have got lost (again?)
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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when we can consider it as a probability, ie the result of deriving it for an infinitely large
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I'd like to see extra added to this page to include mention of climate prediction.
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The word idealization on its own is not clear. For example, it would be an
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be in, which defines a set you can then do analytical calculations on. --
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http://www.opendemocracy.net/globalization-climate_change_debate/2571.jsp
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http://www.opendemocracy.net/globalization-climate_change_debate/2571.jsp
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http://www.climateprediction.net/science/pubs/nature_first_results.pdf
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The point (at least in statistical mechanics) is that the copies are
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Moreover I like to think of the concept of ensemble as being itself
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http://www.opendemocracy.net/content/articles/2571/images/Fig_1.gif
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I have two questions about the actual title of this article:
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Right. But I still don't like "minds" in this definition :)-
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http://www.climateprediction.net/science/strategy_adv.php
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population of possibilities, which he calls an ensemble.
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to consider the system to be made up a large number of
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Why "Statistical ensemble" instead of just "Ensemble"?
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Knowledge level-5 vital articles in
Physical sciences
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Hi IP editor, you're referring to this passage right?
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Yep, you're right, it's a physics term. Let's edit.
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685:
667:74.102.90.54
581:
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62:WikiProjects
45:
1260:fgnievinski
1224:fgnievinski
789:62.53.104.5
783:—Preceding
747:New article
731:62.53.104.5
725:—Preceding
639:—Preceding
332:—Preceding
304:its history
236:Mathematics
227:mathematics
186:Mathematics
1331:Categories
752:article.--
687:prediction
578:ergodicity
293:page were
1311:complete.
857:H-theorem
439:question
50:is rated
1158:Fixed.
1002:. They
1000:not real
859:and the
823:Linuxlad
797:contribs
785:unsigned
739:contribs
727:unsigned
653:contribs
641:unsigned
346:contribs
334:unsigned
1314:Klbrain
1245:Widefox
1145:Eujin16
1121:be bold
1084:Mct mht
973:GChriss
865:imagine
684:Climate
161:on the
134:Physics
125:Physics
81:Physics
52:C-class
1309:Merger
1237:Info:
1160:Jheald
1139:Korean
1125:Nanite
1012:Jheald
989:be in.
930:Jheald
899:Jheald
886:mental
869:mental
855:, the
437:yes-no
295:merged
58:scale.
1215:into
1203:Drake
1200:Jason
1197:Brian
1174:Title
1030:CSTAR
1008:might
987:might
956:CSTAR
913:CSTAR
882:exact
835:CSTAR
754:CSTAR
712:from
645:CSTAR
433:state
422:....
297:into
39:This
1318:talk
1285:talk
1264:talk
1250:talk
1228:talk
1164:talk
1149:talk
1129:talk
1098:talk
1067:talk
1050:talk
890:real
849:real
793:talk
735:talk
698:See
671:talk
649:talk
536:Meas
342:talk
153:High
880:is
490:lim
392:1-
255:???
1333::
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1248:;
1230:)
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1100:)
1069:)
1052:)
817:,
813:,
795:•
780:.
737:•
673:)
651:•
613:
610:Tr
595:σ
584::
539:
516:∑
500:∞
497:→
474:σ
451:,
415:,
384:,
344:•
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561:)
556:k
552:X
548:,
545:E
542:(
531:N
526:1
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520:k
510:N
507:1
494:N
486:=
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480:E
477:(
457:n
453:X
449:E
441:E
428:k
424:X
420:2
417:X
413:1
410:X
394:p
390:p
386:B
382:A
340:(
311:.
263:.
165:.
64::
20:)
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