Talk:Ensemble (mathematical physics)

message: Here's a  suggestion to make the statistical ensemble article more consistent with the quantum statistical mechanics article.  Two relevant operational notions on ensembles are 
* Testing statistical equivalence of ensembles
* Probabilistic sampling from ensembles A, B with probability p 1- p  to form the convex combination of ensembles.
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.
Moreover I like to think of the concept of ensemble as being itself operationally 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 X1, X2 .... Xk... Exactly how this sequential ensemble defines a state 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 yes-no question E (for reference this is discussed in the article quantum logic) we obtain a sequence of measured values (e.g. by observing a dial on a gauge) 
Meas(E, Xn).  Each one of these values is a 0 or 1.  (Of course the measurement process alters the system so it no longer is an instance of the ensemble)
Assume the time average exists
: \sigma(E) = \lim_{N \rightarrow \infty} \frac{1}{N} \sum_{k=1}^N \operatorname{Meas}(E, X_k) 
This is a kind of ergodicity 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 S:
: \sigma(E) = \operatorname{Tr}(E S)   —Preceding unsigned comment added by CSTAR (talk • contribs) 06:32, 12 June 2004
:: 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 equivalence is very good, as well. Dragging in ergodicity seems a little otiose, even worse than dragging in measurements and operationalisablitiy.... 74.102.90.54 (talk) 04:14, 26 November 2015 (UTC)
thread_title:  Statistical ensembles 

message: 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 article.--CSTAR 15:45, 11 Jun 2005 (UTC)
thread_title:  New article 

message: Whatever else, it should be possible to access the usual classical statistical ensembles used by physicists and chemists, namely:-
microcanonical ensemble, canonical ensemble, grand canonical ensemble.
There should be short definitions of the three here, too.
This appears to have got lost (again?) Linuxlad 15:56, 11 Jun 2005 (UTC)
thread_title: mce, ce & gce

message: Why are there two links to the Korean version in the languages box? Does someone know how to edit this - I don't. --Eujin16 (talk) 06:25, 13 March 2009 (UTC)
replies: text: Fixed.  Jheald (talk) 09:08, 13 March 2009 (UTC)
thread_title:  Korean 

message: 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.
I have two questions about the actual title of this article:
* Why "Statistical ensemble" instead of just "Ensemble"?
* Why do we have the unnecessary disambiguation (the parenthetical "mathematical physics" at the end of the title - statistical ensemble redirects here)?
Brian Jason Drake 07:12, 5 May 2009 (UTC)
thread_title:  Title 

message: merge stub subtopic into main article fgnievinski (talk) 15:32, 28 November 2021 (UTC)
replies: text: Klbrain (talk) 13:53, 3 October 2022 (UTC)
thread_title:  Proposed merge of [[Ensemble average]] into [[Statistical ensemble (mathematical physics)]]