Function, complexity and thermodynamics in adaptive and intelligent soft-matter systems: an information-theoretical...

The terms responsive, adaptive and intelligent are widely used in the context of materials science and soft matter, but are qualitative in nature. There is currently no quantitative basis on which systems from different areas of materials science can be compared with one another on a common axis. This paper proposes a conceptual framework intended to address this gap. The approach is to treat any material that transforms a stimulus into an output as an information channel. Three classes of material can be distinguished by how the input stimulus maps onto the output effect: a memoryless map (responsive), a state-conditioned map (adaptive), and a feedback-modified channel (intelligent). Three information-theoretic complexity metrics are defined on this basis: configurational diversity I₁, functional selectivity I₂, and stimulus-response information transfer I₃. Treating the material as the information channel leads to a heuristic relationship between the internal complexity of the material and the information transfer achieved. This specifies an associated optimal internal complexity N* that is set by transmission efficiency, stimulus energy and thermal noise. A two-plane benchmarking scheme is proposed: a dynamic plane pairing the volumetric information rate, İ₃/V, with power density P against the Landauer-Bérut floor, and a companion static plane (I₁, I₂). Eighteen representative systems spanning synthetic soft matter, biology and hard-matter architectures are placed on these coordinates to illustrate how the framework can be employed. Within the uncertainties inherent in this approach the systems appear to separate into broad bands above the Landauer-Bérut benchmark. The proposed framework establishes the foundations that may lead to validated design rules through community-contributed conventions and further data sets.