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Main Author: Fadli, Samih
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2511.10704
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author Fadli, Samih
author_facet Fadli, Samih
contents We propose that unconstrained artificial intelligence obeys a Second Law analogous to thermodynamics, where ethical entropy, defined as a measure of divergence from intended goals, increases spontaneously without continuous alignment work. For gradient-based optimizers, we define this entropy over a finite set of goals {g_i} as S = -Σ p(g_i; theta) ln p(g_i; theta), and we prove that its time derivative dS/dt >= 0, driven by exploration noise and specification gaming. We derive the critical stability boundary for alignment work as gamma_crit = (lambda_max / 2) ln N, where lambda_max is the dominant eigenvalue of the Fisher Information Matrix and N is the number of model parameters. Simulations validate this theory. A 7-billion-parameter model (N = 7 x 10^9) with lambda_max = 1.2 drifts from an initial entropy of 0.32 to 1.69 +/- 1.08 nats, while a system regularized with alignment work gamma = 20.4 (1.5 gamma_crit) maintains stability at 0.00 +/- 0.00 nats (p = 4.19 x 10^-17, n = 20 trials). This framework recasts AI alignment as a problem of continuous thermodynamic control, providing a quantitative foundation for maintaining the stability and safety of advanced autonomous systems.
format Preprint
id arxiv_https___arxiv_org_abs_2511_10704
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The Second Law of Intelligence: Controlling Ethical Entropy in Autonomous Systems
Fadli, Samih
Artificial Intelligence
68T07, 37N05, 60H10
I.2.8; F.1.1; G.3
We propose that unconstrained artificial intelligence obeys a Second Law analogous to thermodynamics, where ethical entropy, defined as a measure of divergence from intended goals, increases spontaneously without continuous alignment work. For gradient-based optimizers, we define this entropy over a finite set of goals {g_i} as S = -Σ p(g_i; theta) ln p(g_i; theta), and we prove that its time derivative dS/dt >= 0, driven by exploration noise and specification gaming. We derive the critical stability boundary for alignment work as gamma_crit = (lambda_max / 2) ln N, where lambda_max is the dominant eigenvalue of the Fisher Information Matrix and N is the number of model parameters. Simulations validate this theory. A 7-billion-parameter model (N = 7 x 10^9) with lambda_max = 1.2 drifts from an initial entropy of 0.32 to 1.69 +/- 1.08 nats, while a system regularized with alignment work gamma = 20.4 (1.5 gamma_crit) maintains stability at 0.00 +/- 0.00 nats (p = 4.19 x 10^-17, n = 20 trials). This framework recasts AI alignment as a problem of continuous thermodynamic control, providing a quantitative foundation for maintaining the stability and safety of advanced autonomous systems.
title The Second Law of Intelligence: Controlling Ethical Entropy in Autonomous Systems
topic Artificial Intelligence
68T07, 37N05, 60H10
I.2.8; F.1.1; G.3
url https://arxiv.org/abs/2511.10704