Information Physics of Intelligence: Unifying Logical Depth and Entropy under Thermodynamic Constraints
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914224526065664 |
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| author | Xu, Jianfeng Li, Zeyan |
| author_facet | Xu, Jianfeng Li, Zeyan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19156 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Information Physics of Intelligence: Unifying Logical Depth and Entropy under Thermodynamic Constraints Xu, Jianfeng Li, Zeyan Information Theory Artificial Intelligence Logic in Computer Science 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. |
| title | Information Physics of Intelligence: Unifying Logical Depth and Entropy under Thermodynamic Constraints |
| topic | Information Theory Artificial Intelligence Logic in Computer Science |
| url | https://arxiv.org/abs/2511.19156 |