Complexity Scaling of Liquid Dynamics

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)PRLTAO0031-900710.1103/PhysRevLett.123.178102; Martiniani et al., Phys. Rev. X 9, 011031 (2019)PRXHAE2160-330810.1103/PhysRevX.9.011031], 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.