Validity of the quasi-stationary pair-distribution closure

Determine the conditions under which the quasi-stationary approximation for the pair distribution function is valid, particularly in systems undergoing phase separation.

Background

The derivation closes the BBGKY-type hierarchy by assuming that the pair distribution function is time independent and can be identified with its steady-state counterpart. The paper characterizes this assumption as crude and notes that its validity is especially uncertain when density inhomogeneities develop during phase separation.

Because the pair distribution function determines the pressure expansion and therefore all coefficients in the resulting scalar field theories, establishing the regime of validity of this closure is necessary for assessing the reliability of the coarse-grained descriptions of interacting active Brownian particles and chiral active Brownian particles.

References

Although the first assumption is often used in the context of active matter, this is crude and is difficult to justify. The second assumption is reasonable when the system remains homogeneous or the density variations occur over sufficiently long lengths. However, the validity of this approximation remains unclear, especially when the system undergoes phase separation.

— Scalar field theory for (chiral) active Brownian particles: bottom-up derivation revisited  (2610.01672 - Kuroda et al., 1 Oct 2026) in Section 2, subsection “Closure approximation”