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

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.

arXiv comment7 pages

References in corpus (4)

• Exchange Monte Carlo Method and Application to Spin Glass Simulations
• The Entropy of the K-Satisfiability Problem
• Number of Magic Squares From Parallel Tempering Monte Carlo
• Entropy-based analysis of the number partitioning problem

Cited by in corpus (8)

• Design of Easily Synchronizable Oscillator Networks Using the Monte Carlo Optimization Method
• Multicanonical MCMC for Sampling Rare Events
• Design of Oscillator Networks with Enhanced Synchronization Tolerance against Noise
• Exploration of Order in Chaos with Replica Exchange Monte Carlo
• Importance Sampling of Rare Events in Chaotic Systems
• Multicanonical Sampling of Rare Trajectories in Chaotic Dynamical Systems
• Thermodynamic Characterization of Synchronization-Optimized Oscillator-Networks
• Role of unstable periodic orbits in phase transitions of coupled map lattices