Isomorphism between Maximum Lyapunov Exponent and Shannon's Channel Capacity

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.