Precise operator-algebraic formulation of the measurement/phase-transition correspondence

Formulate precisely, within an operator-algebraic framework, the correspondence between the emergence of macroscopic states (phase cells) in quantum measurement and phases and phase transitions in statistical mechanics.

Background

The paper draws an analogy between the appearance of macroscopic structures in measurement (phase cells) and the emergence of phases and phase transitions in statistical mechanics, where nontrivial centers arise in von Neumann algebras under physically selected states. It suggests that these two phenomena may be unified in a single operator-algebraic description.

However, the text emphasizes that the exact mathematical formulation of this correspondence is currently lacking and identifies it as an important direction for future research.