What Are the Key Differences Between Virtual and Ordinary Statistical Ensembles?

[A. Neumaier]

Hi Arnold, I found the section about the virtual statistical ensembles from my QM course I took part in Nov-Dec. 2003. It is all written in Romanian, so I need to translate it to German or English. Leave me some time, please. :)

Please translate to English, so that it can be discussed here! I am primarily interested in how the virtual ensemble differs from an ordinary statistical ensemble, i.e., a large collection of actually identically prepared systems.

The latter is the usual ensemble on which one can make statistics by counting, averaging, etc..

The former (the virtual ensemble) is (at least according to Gibbs) one of which you have only a single copy (a single metal bar, say) on which you make the predictions and verify them, while the others copies are just imagined to exist, but never realized. It was Gibbs' trick that enabled him to use (or misuse) the statistical machinery to get results that apply to single macroscopic systems.

 

[dextercioby]

Ok, there was a section of 4 pages which starts from this part right here and expands a little using continuous spectra as well, then relating operational probabilities to operational averages.
So this 1 page should pretty much instruct the eduated reader of what I am/was trying to say in the other thread.