A note on extended locality

Karl Raimund Popper

Svancara, Clinton

This paper forms part of the Relational Field Theory Technical Note Series (0.1–0.3), mapping the continuum from ontological boundary to measurable coherence density. This work extends Notes 0.1–0.2, completing the ontological-to-measurable mapping of Relational Field Theory (RFT). It introduces a relational coherence density metric, ρc = Rc(local) Rc(univ) , bridging micro-coherence (quantum behavior) and macro-coherence (gravitational/cosmological structure). Singularities at ρc → 0 (undefined variation, see Note 0.1) and ρc → ∞ (divergent stability, see Note 0.2) frame this metric, unifying emergent phenomena—quantum decoherence to cosmic acceleration—within a testable ontology for physical transitions Provenance: Originally published on Zenodo (Oct 2025). 10.5281/zenodo.17400900

Masashi Ban, Toshihico Arimitsu

The localized electron-phonon model, which was proposed by Takagahara, Hanamura and Kubo (THK), is extended by including the change of frequency and is treated analytically to obtain the response function and the photon echo signal. Our treatment also gives an analytical expression for the integrand of the transient emission spectrum of the second order optical processes in a localized electron-phonon system which was treated by THK in terms of the eigenvalue problem of the relaxation operator.

Chi-Fang Chen

Quantum many-body Gibbs states satisfy an approximate local Markov property~\cite{chen2025GibbsMarkov}: local noise can be approximately recovered by a quasi-local recovery map, and the conditional mutual information decays for the corresponding tripartition. Recent work~\cite{bergamaschi2025structural} extends this property to approximate stationary states (metastable states) of certain master equations modeling system--bath dynamics, and proposes a strengthened post-selected recovery property requiring recovery to hold for each measurement outcome. In this note, we characterize this \textit{strong Markov property}: it holds if and only if the state additionally satisfies correlation decay for suitable pairs of observables. We further prove several structural and operational consequences of the strong Markov property in the presence of an underlying master equation. First, one can estimate multiple observables from a \textit{single copy} of the state via a repeated measurement--recovery protocol. Second, any two strongly Markov states must have local marginals that are either very close or well separated. Third, if a strongly Markov state can be expressed as a mixture of two strongly Markov states, then their local marginals must be nearly indistinguishable.

Mihaela Moreno Perdomo, Carolina Petersen