Physical justification of the NSO self-consistency criterion

Establish why equality between the relevant local-equilibrium and non-equilibrium statistical-operator averages provides the correct physical criterion for selecting the universal uniform-relaxation regime, and characterize the domain in which this closure assumption is valid.

Background

The non-equilibrium statistical operator (NSO) construction determines its time-dependent thermodynamic parameters by requiring the local-equilibrium (LEQ) and non-equilibrium (NEQ) operators to reproduce the same relevant averages. The paper explains that these matching conditions impose a nontrivial restriction on the underlying microscopic dynamics and are intended to select a universal relaxation regime after microscopic transients and memory of the initial state have decayed.

The authors explicitly question whether scale separation, weakening of initial correlations, and restricting the description to slow variables are sufficient to justify identifying equality of LEQ and NEQ averages with the physical criterion that selects this regime. They therefore regard the self-consistency relations as an additional closure assumption whose physical basis and validity range remain unresolved.