Microscopic origin of the log-normal eigenoperator-entanglement distribution

Determine the microscopic origin of the log-normal eigenoperator-entanglement distribution observed in local Lindbladians, including whether it can be derived from locality, operator growth, or other structural constraints on Liouvillian eigenoperators.

Background

The paper finds that the high-entanglement distribution of local Lindbladian eigenoperators is strongly non-Gaussian and is well described by a log-normal form. This behavior appears in both purely dissipative random Lindbladians and dissipative mixed-field Ising chains, whereas nonlocal Lindbladians and generic non-Hermitian random-matrix ensembles exhibit Gaussian or Haar-like statistics.

Although the numerical evidence identifies the distribution, the mechanism producing its log-normal form is not established. The authors specifically identify locality, operator growth, and other structural constraints as possible sources whose roles remain to be derived or distinguished.

References

An important open question is the microscopic origin of this log-normal distribution. It would be particularly interesting to understand whether it can be derived from locality, operator growth, or other structural constraints on Liouvillian eigenoperators.

— Eigenoperator Entanglement Statistics in Local Lindbladians  (2609.29215 - Hong et al., 24 Sep 2026) in Section 5, “Summary and Outlook”

It also remains to be determined how broadly this behavior extends to other local open quantum systems, including models with conservation laws, higher spatial dimensions, and different forms of dissipation.

— Eigenoperator Entanglement Statistics in Local Lindbladians  (2609.29215 - Hong et al., 24 Sep 2026) in Section 5, “Summary and Outlook”

These results provide strong support for our conjecture that the log-normal distribution is robust to microscopic details and symmetry class, and may represent a universal feature of physical Lindbladians with locality.

— Eigenoperator Entanglement Statistics in Local Lindbladians  (2609.29215 - Hong et al., 24 Sep 2026) in Section 4.2, “Eigenoperator entanglement statistics”