Watts-per-Intelligence Part II: Algorithmic Catalysis
This paper provides a theoretical foundation for understanding the thermodynamic limits of algorithmic speed-ups, relevant to the design of efficient computational systems.
This work develops a thermodynamic theory of algorithmic catalysis, proving that the speed-up from reusable computational structures is bounded by algorithmic mutual information and that installing this information incurs a minimum thermodynamic cost. The framework provides a unified information-thermodynamic constraint on intelligent computation.
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.