Timeliness and perception in digital twinning

Official URL: https://dx.doi.org/10.1109/LCOMM.2026.3690689

Digital twins (DTs) are virtual replicas of physical entities (PEs) that evolve through computation and bidirectional communication. A good Digital Representation (DR) is not only defined by its accuracy at a single instant, but by its sustained synchronization with the Physical Entity (PE), only then can it serve as a true replica. This letter derives fundamental information-theoretic limits on reliable digital twinning under feedback. We introduce the Error–Age Penalty (EAP), a distortion function that accounts for both reconstruction error and the dynamical cost of stale information, thereby extending classical timeliness metrics such as Age of Information. In parallel, we incorporate perceptual fidelity through a Rate–Distortion (RD) function. Building on these formulations, we establish Fano-type converse bounds that link reconstruction reliability to two key quantities: (i) the In-The-Loop (ITL) transmission rate, and (ii) directed information, which measures causal dependence between DR and PE. The resulting inequalities expose explicit tradeoffs among communication resources, model sophistication of the DR, timeliness of updates, and perceptual quality. Numerical results on unstable linear systems illustrate how EAP and RDP sharpen performance predictions beyond classical rate–distortion analysis. These results yield fundamental bounds on the minimal communication rate for reliable digital twinning.