Kubo-Martin-Schwinger-gated imaginary-time reconstruction of time-resolved electronic circular dichroism in organic excitonic aggregates.

Time-resolved electronic circular dichroism (TR-ECD) and time-resolved circular dichroism (TRCD) probe chiral exciton dynamics prepared by an ultrafast pump and interrogated by a weak circular probe. The measured signal is a causal mixed electric-magnetic response, whereas imaginary-time methods require a sufficiently stationary reference. Here, we introduce a Kubo-Martin-Schwinger-gated criterion that determines, at each pump-probe delay, whether the selected TRCD-like response can be represented by a conditional one-exciton Gibbs ensemble or requires explicit real-time or Keldysh dynamics. The diagnostic combines a state-level distance from the conditional reference with an integrated spectral distance for the reciprocal E1-M1 response. We apply the protocol to three literature-constrained Frenkel-exciton models: a Ress-type squaraine-polymer squeezed helix, a cisoid indolenine squaraine B hexamer, and a helical perylene-bisimide stack. The results show that early nonthermal states are non-admissible, whereas intramanifold population relaxation and the decay of coherence memory can open a Matsubara-admissible delay window before complete excited-state recovery. The resulting gate identifies when imaginary-time methods can be used without imposing a stationary description on a genuinely nonequilibrium chiroptical response.