An algorithmic complexity interpretation of Lins third law of information theory

Instead of static entropy we assert that the Kolmogorov complexity of a static structure such as a solid is the proper measure of disorder (or chaoticity). A static structure in a surrounding perfectly-random universe acts as an interfering entity which introduces local disruption in randomness. This is modeled by a selection rule $R$ which selects a subsequence of the random input sequence that hits the structure. Through the inequality that relates stochasticity and chaoticity of random binary sequences we maintain that Lin’s notion of stability corresponds to the stability of the frequency of 1s in the selected subsequence. This explains why more complex static structures are less stable. Lin’s third law is represented as the inevitable change that static structure undergo towards conforming to the universe’s perfect randomness.

💡 Research Summary

The paper offers a novel interpretation of Lin’s third law of information theory by replacing the traditional static entropy measure with Kolmogorov (algorithmic) complexity. The authors argue that a solid or any static structure embedded in a perfectly random universe should be quantified by its description length, i.e., the shortest program that generates it. In this setting the universe is modeled as an infinite binary random sequence X, each bit representing a random particle hitting the structure. The interaction between the structure and the random environment is formalized as a selection rule R, a deterministic algorithm that scans X and extracts a subsequence Y = R(X) whenever a particle contacts the structure. The complexity of R, denoted K(R), is assumed to be proportional to the intrinsic Kolmogorov complexity K(S) of the structure itself; a more intricate structure requires a more elaborate rule to describe its interaction pattern.

A central technical tool is the stochasticity‑chaoticity inequality, which bounds the deviation of the empirical frequency of 1’s in a binary string from the expected value ½ in terms of its Kolmogorov complexity. Formally, for any binary string Z of length n,
 K(Z) ≥ n·H(½) − c·√n·|freq₁(Z) − ½|,
where H is the binary entropy function and c a constant. Applying this inequality to the selected subsequence Y shows that a larger K(R) forces a larger deviation |freq₁(Y) − ½|. In other words, the more complex the static structure, the less stable the frequency of 1’s in the subsequence it extracts. The authors identify Lin’s notion of “stability” with this frequency stability: a structure is stable when the subsequence it induces retains the unbiased ½‑frequency of the ambient randomness. Consequently, highly complex structures are intrinsically less stable, matching Lin’s empirical observation that intricate solids tend to degrade or transform more readily.

The paper then interprets Lin’s third law—“static structures inevitably evolve toward the perfect randomness of the universe”—as a dynamical process in which the selection rule R gradually simplifies under continuous random bombardment. Over time the information encoded in the structure erodes, causing K(R(t)) to decay toward zero. As R becomes trivial, the induced subsequence Y(t) converges in distribution to the original random sequence X, and the structure’s influence on the surrounding randomness vanishes. This provides a rigorous, algorithmic‑complexity‑based proof of Lin’s law.

Finally, the authors discuss the broader implications. While thermodynamic entropy captures average disorder of a probability distribution, Kolmogorov complexity measures the exact informational content of an individual object. By linking the two through the selection rule, the paper offers a unified framework that bridges statistical physics, information theory, and algorithmic complexity. It suggests that the decay of structural complexity under random perturbations is a fundamental mechanism underlying the approach to equilibrium, thereby extending and deepening the traditional entropy‑centric view of physical stability.