<span class="mw-page-title-main">Goldstein06a</span>
Fabrice P. Lauss𝕪s inelike Web

Canonical Typicality. S. Goldstein, J. Lebowitz, R. Tumulka and N. Zanghì in Phys. Rev. Lett. 96:050403 (2006).  What the paper says!?

A short two-and-a-half letter which justifies the canonical ensemble in quantum mechanics as arising not from assumptions on ergodic ignorance, but high-dimensional features that project almost any pure state of the system + bath system in the microcanonical description, into a mixed canonical density matrix. The authors refer to this as "canonical typicality". The reduced density matrix is, typically, canonical:

In this Letter [...] we prove that, in the thermodynamic limit, the reduced density matrices of the overwhelming majority of the wave functions of S+B are canonical. We call this statement canonical typicality. As a consequence of canonical typicality, it follows that the canonical ensemble is even more inevitable in quantum mechanics— arising as it does there without the invocation of any genuine randomness—than it is classically.

Their first column gives the textbook argument for Eq. (1).

The last part concludes with comparisons with Schrödinger who seems to have arrived to essentially the same results without making a big deal of it, and H. Tasaki but who got a weaker, long-time version.

This is an interesting text but that relies on the system + bath divide. In connection to our interest of ergodicity breaking, this might be relevant but with time coming back to provide a surrounding to each system (each frame in our case).