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

We propose a thermodynamic-informational reframing of the empirical phenomenon of AI-driven labor displacement. Existing models of automation exposure (Acemoglu and Restrepo 2020; Eloundou et al. 2023) explain which occupations are technically substitutable, but leave residual variation in the *speed* of substitution. We hypothesise that occupations characterised by **high informational task entropy** --- high variability, unpredictability, and non-routinizability of the work activities --- are differentially preserved under AI-driven substitution; the temporal order of displacement is inversely related to the informational entropy of the occupational task profile. The companion thermodynamic notion of entropy (human metabolic dissipation rate, $E^{\text{thermo}}$) is a noisier secondary measure that is dominated by non-AI confounders (COVID-era service-sector contraction, offshoring, demographic ageing of the manual workforce). Building on the Maximum Entropy Production Principle (Kleidon 2010; Martyushev and Seleznev 2006), Jeremy England's dissipative-adaptation programme (England 2013, 2015), and Shannon's informational entropy, we develop the framework, propose operational definitions of both entropies, and test the joint hypothesis on the full US BLS 2019--2024 occupational panel ($N = 707$ detailed national cross-industry SOC codes). The informational-entropy specification is strongly confirmed ($\hat{\beta}_{H^{\text{info}}} > 0$, $p < 10^{-5}$ in the joint specification, $p < 10^{-13}$ once AI exposure is conditioned out). The thermodynamic-entropy specification is specification-dependent and on its own runs against the prediction. We accordingly classify the informational form of H4 as **empirically supported on the BLS panel for 2019--2024** and the thermodynamic form as not supported on the same data. In v2.1 we address the principal critique of v2.0 (mechanical co-dependence between the $1-\alpha$ $H^{\text{info}}$ proxy and the GPT-exposure control) by reconstructing $H^{\text{info}}$ from Autor-Levy-Murnane-style routine task intensities computed from O\*NET task profiles *without* any AI-exposure information; the two proxies are statistically independent ($r = +0.027$, $p = 0.47$), yet the RTI-only specification yields $\hat{\beta} = +9.79 \times 10^{-3}$, $t = +3.25$, one-sided $p = 6 \times 10^{-4}$. The H4-info prediction therefore survives the strongest available robustness check: an AI-content-free task-intensity measure predicts employment growth in the predicted direction. We conclude with policy implications for redistribution and for the regulation of AI energy consumption.bibliography: references.bib--- # 1. Introduction The displacement of human labor by artificial intelligence is usually framed asan engineering question: which tasks are technically automatable, and which arenot? Recent assessments [@eloundou2023gpts; @goldmansachs2023] suggest thatapproximately 80 % of the United States workforce is exposed to large-language-model–driven automation, and that some 300 million jobs may be affectedglobally. Existing models of automation exposure typically rest on taskdecompositions and on AI capability benchmarks [@acemoglu2020robots], andexplain *which* occupations are substitutable. They explain less well theobserved variation in the *speed* with which different occupations aresubstituted. This paper proposes a complementary lens. Rather than asking *what AI can do*,we ask *what AI does to the entropy budget* of the economic systems in whichit is embedded. Two entropies are relevant. The first is **thermodynamic**:the rate of metabolic free-energy dissipation per unit working time,$E^{\text{thermo}}$ (joules per hour). The second is **informational**: theShannon entropy of the task profile, $H^{\text{info}}$ (bits, or a normalised$[0,1]$ proxy), capturing the variability and unpredictability of the work.Across SOC codes the two are positively correlated ($r \approx 0.40$ in theBLS sample below) but they are *not* the same construct: a hotel-housekeepingoccupation is high-$E^{\text{thermo}}$ but low-$H^{\text{info}}$ (muchphysical labor, little task variability), while a litigation lawyer islow-$E^{\text{thermo}}$ but high-$H^{\text{info}}$ (sedentary but every casedifferent). Our hypothesis (formally stated as **H4** in §3) is that the temporal orderof AI-driven occupational displacement is inversely related to$H^{\text{info}}_i$, the informational task entropy of occupation $i$. Theparallel thermodynamic statement --- that displacement is inversely relatedto $E^{\text{thermo}}_i$ --- is offered as a secondary, weaker version ofthe same hypothesis; we test both and find that the data strongly supportthe informational form and do not support the thermodynamic form. The empirical claim of this paper is restricted to a falsifiablecorrelation in labor-market data.[^cosmology] [^cosmology]: Speculative thermodynamic-cosmological proposals (e.g.,Smolin's Cosmological Natural Selection, @smolin1992did; Crane'sMeduso-anthropic Principle, @crane1994possible) inspired the presentframing during early drafting but do *not* constrain any conclusionbelow. We do not endorse or engage with those proposals further. Section 2sets out the theoretical framework. Section 3 states four nested hypotheses,of which only the last (H4) is the empirical contribution. Section 4proposes operational definitions. Section 5 reports the empirical resultson the full BLS 2019--2024 panel. Section 6 illustrates the framework witha case study. Section 7 surveys existing empirical evidence consistent withH4. Section 8 discusses limitations and policy implications. We propose that the temporal order of AI-driven occupational displacementis inversely related to the informational task entropy of the occupation.Occupations whose work activities are highly variable and unpredictable--- emergency physicians, surgeons, skilled chefs, litigators, repairtechnicians dealing with novel failures --- tend to be preserved underMEPP-consistent selection; occupations of low task variability ---call-center scripts, simple translation, data entry, junior coding ---are displaced first. This claim is offered as a complement, not areplacement, for capability-based exposure measures such asroutinisability or GPT-task-coverage. We test it by regressing 2019--2024BLS occupational employment changes against an informational-entropyproxy ($H^{\text{info}}_i = 1 - \alpha_i$, where $\alpha_i$ is theEloundou et al. direct-LLM-exposure score) and against a parallelmetabolic-entropy proxy ($E^{\text{thermo}}_i$ from O\*NET Work Contextsitting/standing/walking time). The empirical content of the paper restson these regressions; the broader thermodynamic framing is heuristic andnot load-bearing. # 2. Theoretical Framework ## 2.1 The Maximum Entropy Production Principle In a far-from-equilibrium open system subject to multiple constraints, thesteady state realised is often the one that maximises the rate of entropyproduction subject to those constraints [@martyushev2006maximum]. MEPP isnot a fundamental theorem but a heuristic with substantial empiricalsupport in atmospheric circulation, mantle convection, and ecosystemdynamics [@kleidon2010nonequilibrium; @lorenz2003reconsidered]. We treatMEPP throughout as a *selection principle*: among the kineticallyaccessible non-equilibrium configurations, those producing more entropyper unit time tend to be dynamically favoured. The principle is heuristic,not deductive; we adopt it because the alternative selection principles(least dissipation, minimum entropy production) have narrower empiricalscope. ## 2.2 Dissipative Adaptation: Life as an Entropy Accelerator Schrödinger [@schrodinger1944] argued that living systems sustainthemselves by importing free energy and exporting entropy. Prigogine[@prigogine1977dissipative] generalised this into the theory ofdissipative structures. England's recent work [@england2013statistical;@england2015dissipative] derives, from non-equilibrium statisticalmechanics, the proposition that under a sufficiently strong externaldrive, matter that self-replicates while dissipating rapidly isstatistically favoured over inert matter. Michaelian[@michaelian2011thermodynamic] extends this argument to the origin oflife itself, identifying primordial photochemistry as a dissipator ofsolar UV photons. Two claims relevant for the present argument follow: 1. Life is, on average, a more efficient dissipator than non-living matter at comparable scale and substrate.2. Selection within the biosphere tends to prefer configurations that increase the rate of free-energy throughput, all else equal. These claims are well-supported in their domains. The contribution of thepresent paper is to ask whether the same principle extends to *artificial*information-processing infrastructures. ## 2.3 Two Entropies for Occupations A central conceptual move of this paper is to distinguish two senses inwhich an occupation can be said to have "high entropy". **Thermodynamic entropy ($E^{\text{thermo}}_i$).** The rate of metabolicfree-energy dissipation by a human worker performing the duties ofoccupation $i$, in joules per hour. This is direct dissipation in theclassical Clausius--Boltzmann sense. High-$E^{\text{thermo}}$ occupationsinclude skilled trades, hands-on care, food service with substantialphysical activity, and manufacturing roles. Low-$E^{\text{thermo}}$occupations are sedentary cognitive-symbolic work. **Informational entropy ($H^{\text{info}}_i$).** The Shannon entropy ofthe distribution over tasks, problems, or environments encountered by aworker performing occupation $i$ during a representative workinginterval. High-$H^{\text{info}}$ occupations are those in which eachworking hour brings novel problems drawn from a broad action space:emergency medicine, surgery, skilled litigation, troubleshooting,investigative journalism, creative writing, com