Computation of the Kolmogorov-Sinai entropy using statistitical mechanics: Application of an exchange Monte Carlo method

TL;DR

This paper introduces a novel method to compute the Kolmogorov-Sinai entropy of chaotic systems by leveraging statistical mechanics and an exchange Monte Carlo approach, enabling analysis of complex chaotic dynamics.

Contribution

It presents a new approach to calculate KS entropy using a Hamiltonian with many ground states derived from chaotic evolution equations, employing an exchange Monte Carlo method.

Findings

Successfully computed KS entropy for a chaotic repeller

Demonstrated the method's applicability to systems with complex ground state landscapes

Provided a new link between chaos theory and statistical mechanics

Abstract

We propose a method for computing the Kolmogorov-Sinai (KS) entropy of chaotic systems. In this method, the KS entropy is expressed as a statistical average over the canonical ensemble for a Hamiltonian with many ground states. This Hamiltonian is constructed directly from an evolution equation that exhibits chaotic dynamics. As an example, we compute the KS entropy for a chaotic repeller by evaluating the thermodynamic entropy of a system with many ground states.