Watts-per-Intelligence Part II: Algorithmic Catalysis

2026-04-21

AI Summary

This work addresses the high energy consumption in intelligent computing arising from irreversible operations across task classes by proposing an energy-efficient approach grounded in reusable computational structures. By developing a thermodynamic theory of algorithmic catalysis, the study establishes an upper bound relating algorithmic mutual information to task descriptors and derives a lower bound on the energetic advantage over catalyst deployment cycles, thereby unifying information-theoretic and thermodynamic constraints on intelligent computation. The framework is validated on the affine SAT task class, revealing that current learning systems are fundamentally governed by a unified information–thermodynamics trade-off. Using “watts per intelligence” as a metric, the method achieves substantial energy savings for specific task classes.

Technology Category

• Machine Learning: Information Theory
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• algorithmic catalysis
• thermodynamic cost
• irreversible operations
• algorithmic mutual information
• intelligent computation

Innovation

• algorithmic catalysis
• thermodynamic cost
• Landauer erasure
• algorithmic mutual information
• watts-per-intelligence