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

The work argues that terms like responsive, adaptive, and intelligent in soft matter are often used qualitatively, making it hard to compare different systems. It proposes modeling any stimulus-coupled material as an information channel and classifying system behavior by how the input-output mapping depends on internal state and feedback. It introduces three information-theoretic metrics: configurational diversity (I1), functional selectivity (I2), and stimulus-response information transfer (I3). It also discusses how internal complexity can relate non-monotonically to realized information transfer because of limits set by transmission efficiency, stimulus energy, and thermal noise. To compare systems across fields, the authors propose two benchmarking plots: a dynamic plane using information transfer rate versus power density (referenced to a Landauer-Berut floor) and a static plane using I1 and I2. They report that sixteen example systems from synthetic soft matter, biology, and hard matter fall into broad bands above the benchmark, with uncertainty of about one to two decades per axis.