Isomorphism between Maximum Lyapunov Exponent and Shannon's Channel Capacity

2017/06/26 by Gerald Friedland, Friedland, Gerald, Alfredo Metere +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Computability, Logic, AI Algorithms #Computational Physics (physics.comp-ph) #Evolutionary Algorithms and Applications #FOS: Computer and information sciences #FOS: Physical sciences #Gaussian Processes and Bayesian Inference #Information Theory (cs.IT) #Neural Networks and Applications #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #cond-mat.stat-mech #cs.IT #math.IT #physics.comp-ph

paper · pdf · doi:10.48550/arxiv.1706.08638

Submitted to Phys. Rev. Lett

openalex publication_date 2017/06/26 · arxiv created 2018/01/25 · arxiv updated 2018/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We demonstrate that the Maximum Lyapunov Exponent for computable dynamical systems is isomorphic to the maximum capacity of a noiseless, memoryless channel in a Shannon communication model. The isomorphism allows the understanding of Lyapunov exponents in the simplified terms of Information Theory, rather than the traditional definitions in Chaos Theory. This work provides a bridge between fundamental physics and Information Theory to the mutual benefit of both fields. The result suggests, among other implications, that machine learning and other information theory methods can be successfully employed at the core of physics simulations.

Cited by

• Principle of Conservation of Computational Complexity

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