Subjective Time from Memory and Energy: The Flow Bound

We propose an operational framework in which subjective time is not a primitive parameter but an informational ordering: it arises from the monotone growth of the mutual information F = I(O:M) between an observer and its memory register, under the class of memory-writing instruments (fresh registers, persistent records) for which this functional is provably non-decreasing. The central result is an upper bound on the rate at which F can grow along a Lindblad trajectory, expressed in terms of the energetic variance accessible to the observer, a measurement-induced memory-writing term, and the Bures norm of the true Riemannian gradient of F — not a quantum Fisher information of the informational generator, which enters separately through the Mandelstam–Tamm speed bound. The bound is derived from first principles; it is not an ansatz. When both the visible energetic variance and the measurement term vanish, monotonicity forces the informational rate to zero: subjective time freezes. We extend the single-observer picture to cohorts of observers sharing memory redundancy, showing — under a Kuramoto-type coupling ansatz and a homogeneous mean-field approximation, whose phenomenological status is explicitly acknowledged — that informational redundancy drives exponential convergence of individual subjective times toward a common rate. The paper includes a brief interpretive discussion of the block-universe and internal-observer viewpoints, and proposes qubit-agent protocols for experimental falsification.