Local Curvature of Quantum Information: Survival Expansion, Entanglement Flux, and the Arrow of Time

We develop a geometric framework — Local Curvature of Quantum Information (LCQI) — for analysing open quantum dynamics through the short-time expansion of the survival probability. The expansion defines three local coefficients (tilt, curvature, jerk j) that cleanly separate dissipative from unitary contributions in a model-independent way. The tilt governs the onset of irreversibility: it equals half the purity-loss rate, controls the logarithmic singularity Sₕ₍ (t) = -\, t t + O (t) of von Neumann entropy production, and connects to Bures distance and quantum Fisher information. For non-Markovian dynamics, sign changes in (t) witness information backflow. For multipartite systems, the entanglement-flux decomposition Q = ₓ₎ₓ₀₋ + 12ĖL (0) shows that local irreversibility splits exactly into global dissipation plus entanglement production, with N-partite generalisations. Combining this with the entropy singularity yields a decomposition of thermodynamic entropy production into a singular entanglement-driven component and a finite Clausius heat term.