Watts-per-Intelligence Part II: Algorithmic Catalysis

TL;DR

This paper introduces a thermodynamic theory of algorithmic catalysis, linking computational efficiency with information-theoretic and thermodynamic costs, and applies it to intelligent systems.

Contribution

It develops a unified framework connecting thermodynamics, information theory, and computation, providing bounds on speed-up and energy costs for algorithmic catalysis.

Findings

Speed-up bounded by mutual information between substrate and class descriptor.

Thermodynamic cost of installing class-specific information via Landauer erasure.

Coupling theorem relates deployment horizon to energetic favorability of catalysts.

Abstract

We develop a thermodynamic theory of algorithmic catalysis within the watts-per-intelligence framework, identifying reusable computational structures that reduce irreversible operations for a task class while satisfying bounded restoration and structural selectivity constraints. We prove that any class-specific speed-up is upper-bounded by the algorithmic mutual information between the substrate and the class descriptor, and that installing this information incurs a minimum thermodynamic cost via Landauer erasure. Combining these results yields a coupling theorem that lower-bounds the deployment horizon required for a catalyst to be energetically favourable. The framework is illustrated on an affine SAT class and situates contemporary learned systems within a unified information-thermodynamic constraint on intelligent computation.