Watts-per-Intelligence Part II: Algorithmic Catalysis

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 encoding 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 an algorithmic catalyst to be energetically favourable. The framework is illustrated on an affine SAT class and situates contemporary learned systems within an information thermodynamic constraint on intelligent computation.