Information Physics of Intelligence: Unifying Logical Depth and Entropy under Thermodynamic Constraints

TL;DR

This paper introduces a unified thermodynamic framework for understanding information processing in AI, linking logical depth and entropy, and revealing a phase transition that guides optimal strategies between memory retrieval and generative computation.

Contribution

It proposes a novel physical framework and a new metric, Derivation Entropy, to analyze the thermodynamic costs of information processing in AI models.

Findings

Identification of a critical phase transition point between memory retrieval and generative computation.

Introduction of the 'Energy-Time-Space' conservation law explaining AI efficiency.

Derivation of a mathematical bound for energy-efficient AI architecture design.

Abstract

The rapid scaling of artificial intelligence models has revealed a fundamental tension between model capacity (storage) and inference efficiency (computation). While classical information theory focuses on transmission and storage limits, it lacks a unified physical framework to quantify the thermodynamic costs of generating information from compressed laws versus retrieving it from memory. In this paper, we propose a theoretical framework that treats information processing as an enabling mapping from ontological states to carrier states. We introduce a novel metric, Derivation Entropy, which quantifies the effective work required to compute a target state from a given logical depth. By analyzing the interplay between Shannon entropy (storage) and computational complexity (time/energy), we demonstrate the existence of a critical phase transition point. Below this threshold, memory retrieval is thermodynamically favorable; above it, generative computation becomes the optimal strategy. This "Energy-Time-Space" conservation law provides a physical explanation for the efficiency of generative models and offers a rigorous mathematical bound for designing next-generation, energy-efficient AI architectures. Our findings suggest that the minimization of Derivation Entropy is a governing principle for the evolution of both biological and artificial intelligence.