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arXiv · 2605.19795

Function, Complexity and Thermodynamics in Adaptive and Intelligent Soft Matter Systems: An Information-Theoretical Framework

George S. Attard
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Abstract

The terms responsive, adaptive and intelligent are widely used in soft matter and materials science but remain qualitative, with no quantitative basis for comparing systems from different areas on a common axis. We address this by treating any stimulus-coupled material as an information channel. The three classes are distinguished by kernel conditioning: a memoryless map p(y|x) (responsive), a state-conditioned map p(y|x,s) (adaptive), and a feedback-modified channel with memory (intelligent). Three information-theoretic metrics follow: configurational diversity I1, functional selectivity I2, and stimulus-response information transfer I3. Because the kernel and substrate are the same object, a heuristic non-monotonic relationship arises between internal complexity and realised information transfer, with an optimal complexity N* set by transmission efficiency, stimulus energy and thermal noise. We propose two benchmarking planes: a dynamic plane (volumetric information rate I3/V versus power density P, referenced to the Landauer-Berut floor) and a static plane (I1, I2). Sixteen systems spanning synthetic soft matter, biology and hard matter separate into broad bands above the benchmark: ~10^18-10^20x for soft matter and shape-memory alloys, 10^10-10^16x for silicon and electromechanical devices, 10^9-10^10x for neuromorphic memristors, and 10^5-10^8x for evolved biology, with an ER lipid network near 10^11x. Each placement carries an uncertainty of one to two decades per axis; the band ordering nonetheless appears robust. The gap between synthetic soft matter and biology is tentatively attributed to the per-element substrate energy scale (1-10 kBT versus 10^4-10^5 kBT). The framework is offered as a foundation that may lead to validated design rules; three routes are proposed by which soft matter's separation from the Landauer benchmark might be reduced.

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George S. Attard. 2026-05-19. Function, Complexity and Thermodynamics in Adaptive and Intelligent Soft Matter Systems: An Information-Theoretical Framework. https://arxiv.org/abs/2605.19795

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