Entropy Estimation of Ferromagnetic Models via Lossless Compression

Abstract

Entropy calculations are essential for determining the level of randomness of a system. Numerical methods for entropy estimation of equilibrium systems is a developing field. We apply the Lempel-Ziv 77 lossless compression algorithm to the thermodynamically equilibrated 2-dimensional Ising model configurations generated via Markov-Chain Monte Carlo (MCMC) simulations, and show that the information content of the system, measured via its computable information density (CID), is directly proportional to the entropy of the system, thus providing accurate estimates for the thermodynamic entropy. This numerical method for entropy estimation can be further applied to systems for which analytical solutions are unknown.