Complexity Scaling of Liquid Dynamics

TL;DR

This paper demonstrates that the diffusion coefficients of simple liquids can be predicted from the Kolmogorov complexity of a single equilibrium configuration, establishing a quasiuniversal exponential relationship.

Contribution

It introduces a novel complexity scaling approach linking entropy estimation via compression to liquid dynamics, enabling property prediction from minimal data.

Findings

Diffusion coefficients follow a quasiuniversal exponential function of compression length.

Entropy estimated from optimal compression correlates with liquid dynamics.

Complexity scaling can estimate dynamic properties from a single configuration.

Abstract

According to excess-entropy scaling, dynamic properties of liquids like viscosity and diffusion coefficient are determined by the entropy. This link between dynamics and thermodynamics is increasingly studied and of interest also for industrial applications, but hampered by the challenge of calculating entropy efficiently. Utilizing the fact that entropy is basically the Kolmogorov complexity, which can be estimated from optimal compression algorithms [Avinery et al., Phys. Rev. Lett. 123, 178102 (2019); Martiniani et al., Phys. Rev. X 9, 011031 (2019)], we here demonstrate that the diffusion coefficients of four simple liquids follow a quasiuniversal exponential function of the optimal compression length of a single equilibrium configuration. We conclude that "complexity scaling" has the potential to become a useful tool for estimating dynamic properties of any liquid from a single configuration.