Informational Task Entropy and the Selection of Occupations Under AI-Driven Substitution

We propose a thermodynamic-informational reframing of AI-driven labor displacement. We hypothesise that occupations of high informational task entropy H_info are differentially preserved under AI-driven substitution. The hypothesis is tested on four triangulated panels: US BLS occupational (N=707), US state×occupation (N=27,356), and EU-32 ISCO cross-country at 1- and 2-digit resolutions (N=315, 1,198). An AI-content-free H_info proxy reconstructed from Autor-Levy-Murnane routine-task intensities (O*NET, independent of any AI-exposure data) yields beta>0 at p<10^-3 alone and p<10^-13 in the cross-country panel with country fixed effects. A pre-trends placebo on four sliding 5-year windows (2011-2024) shows the gradient was stable from 2011 to 2019 and statistically significantly accelerated only in 2019-2024, the window containing the post-ChatGPT generative-AI surge (DDD interaction t=+3.38, p_one=4×10^-4). Approximately 60% of the post-period coefficient is AI-attributable acceleration; the residual 40% is the pre-existing long-run routinizability gradient documented in classical labour economics. Two independent country-level AI instruments (Eurostat 2025 GenAI usage and WIPO AI patents 2021) both find the gradient stronger in AI-laggard than AI-frontier countries, consistent with a substitution-rate-of-residual-routine-stock mechanism. Companion Informational Resilience Index (IRI) for 698 US occupations and full reproducible code at https://github.com/semini080220-ship-it/entropy-ai-paper. Robustness checks across eight proxies in the Appendix.