Eidos temporal: open quantum dynamics as a geometric flow with a curvature constraint on the space of quantum states
DOI:
https://doi.org/10.70577/asce.v5i3.1108Keywords:
open quantum systems; GKSL equation; Bures geometry; qubit; nonlinear dynamics; information geometry; decoherence; geometric flow.Abstract
The Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation provides the standard description of a broad class of open quantum systems in the Markovian regime. This work explores a complementary hypothesis: that the intrinsic geometry of the space of quantum states can be used to build an additional dynamical term, keeping GKSL as a null model rather than a theory to be replaced. Eidos Temporal is formulated as a phenomenological geometric flow on the state space of a qubit, using the Bures metric and a contraction of the Ricci tensor with the velocity field of the reference dynamics. For a full-rank qubit one obtains explicitly Ric = 8g and R = 24, corresponding to a constant sectional curvature geometry K = 4. The proposed corrector is the gradient of a curvature scalar built from the GKSL flow. In a radial reduction, the resulting dynamics is ṙ = −[Γ + 8τEΓ²/(1 − r²)]r, so that the effective rate is state-dependent. For Γ = 1.2/µs, τE = 0.012 µs and r0 = 0.9999, numerical integration yields ΔP_max = 0.0485926 at t ≈ 0.337 µs. The quantity Y(t) = ln[P(t) − P_th] is introduced, which is exactly linear for constant-rate GKSL and shows curvature for Eidos. A free-rate GKSL fit gives Γ_fit ≈ 1.3773/µs but does not reproduce the Eidos curvature. The result establishes a discrimination test against a simple constant renormalization of the rate. The mathematical viability of the radial trajectory is demonstrated for the parameters studied; complete positivity, the microscopic derivation of τE and thermodynamic consistency remain open and explicitly delimited questions.
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