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arXiv · 2610.24017

Causal Information Exchange as a Necessary Condition for Adaptive Regulation: A Perturbational Framework for Life and Agency

Brian LuValle·Abicumaran Uthamacumaran·Hector Zenil
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Abstract

Information exchange can support living organisation without providing a sufficient criterion for life. We develop a perturbational framework that distinguishes causal transmission, directional imbalance, internal retention, response structure and functional regulation. Randomised interventions define Shannon information channels; for deterministic binary recipients, their context-conditioned mutual information is exactly a paired perturbation-response indicator. Spatial and temporal averages of these local channels measure information-exposure density, rather than joint information or conserved information flux. Complementary Coding Theorem Method and Block Decomposition Method (BDM) estimates describe response and trajectory structure. A same-shaped zero-mask reference separates raw BDM from a structural contrast; neither is a channel mutual information. Retained exploratory BDM plots are distinguished from the normalised causal-channel results. Retention-weighted coupling and directionality obey algebraic bounds, and ensemble reciprocity need not imply reciprocity within individual contexts. For a specified binary sensor--internal-channel--actuator task, we derive a positive information lower bound from successful regulation and construct controllers with identical information profiles but opposite functional outcomes. A study of 2,000 ordered elementary-cellular-automaton rule pairs, six detailed examples, recurrence and lossless coding analyses, and a signed-network extension demonstrates dissociations among perturbational responsiveness, structural regularity and recurrence. The results establish causal information as a necessary resource for the stated form of adaptive regulation, while showing why neither causal coupling nor response complexity alone measures agency or life.

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Brian LuValle, Abicumaran Uthamacumaran, Hector Zenil. 2026-10-16. Causal Information Exchange as a Necessary Condition for Adaptive Regulation: A Perturbational Framework for Life and Agency. https://arxiv.org/abs/2610.24017

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