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Abstract

This paper investigates the emergence of classical objectivity in quantum systems through the measure of Functional Information in Quantum Darwinism ($FI_{QD}$). The goal is to quantify objectivity as the abundance of environment fragments that independently contain sufficient information about a system's pointer states. The method relies on the Holevo quantity -- an upper bound on accessible information -- and introduces a tolerance criterion called $\delta$-adequacy, where fragments are considered adequate if they retain at least $(1-\delta)H_S$ bits of pointer information. Numerical simulations of a dephasing model with fragment sampling reveal three robust features: (i) an early-time regime where $\log R_\delta(t)$ grows approximately linearly, (ii) capacity-limited plateaus determined by fragment size and environment dimension, and (iii) stability of the onset criterion under different sampling strategies and overlap corrections. These results establish $FI_{QD}$ as a practical and conservative yardstick for operational objectivity. Beyond numerical findings, the analysis links redundancy growth to thermodynamic costs of record formation and interprets $FI_{QD}$ as a resource monotone under noisy dynamics. The study suggests that classical objectivity emerges not as an assumption but as a quantifiable, resource-limited abundance of redundant records.