Entropy production control of BKM non-normality

Determine whether a suitable quantum steady-state entropy production ss controls the BKM non-normality of the induced tangent-space generator through a bound of the form [,] F(ss).

Background

The induced tangent-space generator is decomposed into BKM-symmetric and BKM-antisymmetric parts. Their commutator, equivalently the BKM non-normality [,], determines the leading nonequilibrium curvature correction. The paper emphasizes that this geometric non-normality and thermodynamic entropy production are distinct quantities.

Beyond bounding the transport activity by entropy production, the authors leave unresolved the stronger question of whether entropy production can control the generator-level norm of the BKM non-normality itself. Such a result would provide a direct thermodynamic constraint on the geometric mechanism governing short-time relaxation curvature.

References

A further open question is whether \sigma_{\rm ss} itself controls the BKM non-normality, |[\mathcal{K}\ddagger,\mathcal{K}]|\le F(\sigma_{\rm ss}).

— Information-geometric bounds on nonequilibrium relaxation in quantum Markov dynamics  (2609.09599 - Guo et al., 9 Sep 2026) in Section 8, Conclusion and outlook