Watts-per-Intelligence Part II: Algorithmic Catalysis

arXiv cs.AI / 4/25/2026

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Key Points

The paper proposes a thermodynamic framework for “algorithmic catalysis” within the watts-per-intelligence model, focusing on reusable computational structures that cut down irreversible operations for a task class.
It shows that class-specific speed-ups are theoretically limited by the algorithmic mutual information between the computational substrate and the class descriptor, linking performance to information content.
The authors argue that storing/using this class information requires a minimum thermodynamic cost, grounded in Landauer’s principle for erasing information.
By combining these results, the paper derives a “coupling theorem” that sets a lower bound on how long a catalyst must be used (deployment horizon) before the energy cost is worthwhile.
An example using an affine SAT problem class is provided to illustrate the framework and to connect learned systems to information–thermodynamic constraints on intelligent computation.

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.