English

Toward a Categorical Foundation for Energetically Coherent Computation

This paper proposes a shift from the dominant paradigm of layered abstraction to a resource-sensitive model grounded in category theory. The author argues that the current "separation-of-concerns" principle acts as an energetically forgetful functor, discarding vital structural information that cannot be recovered through high-level profiling. Key Theoretical Contributions: The Energetically Coherent Adjunction: Defines the relationship between an Algorithmic Category (A) and a Physical Category (P) through a realization functor F and an abstraction profunctor G. Interaction Term (Γ) and Phase Transitions: Identifies that at large compositional depths, energetic interaction terms (Γ) become dominant, explaining why micro-benchmarks often fail to predict full-scale application energy profiles. Information-Energy Entanglement: Utilizes Landauer’s Principle to show that energetic structure is entangled with information-theoretic structure, requiring cost-preserving functors to track entropy production per morphism. Thermodynamic Redefinition of Correctness: Proposes that a computation is "correct" only if it satisfies both its input-output specification and remains within a controlled

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