The Parameterless Fit

Supercooled liquids approaching the glass transition slow down by orders of magnitude. Fitting the dynamics — the mean-squared displacement as a function of time in the deeply viscous regime — requires a model. The von Schweidler law, widely used, has one dimensionless free parameter. The random barrier model has zero.

The random barrier model fits better.

Using particle-swap Monte Carlo combined with GPU molecular dynamics on a ternary Lennard-Jones glass former, the random barrier model — which pictures dynamics as hopping over randomly distributed energy barriers — reproduces the inherent mean-squared displacement more accurately than the von Schweidler expression across the extremely viscous regime. More practically, it predicts diffusion coefficients from short-time simulation data more reliably.

The through-claim: having fewer free parameters is not a tradeoff against accuracy. It’s a structural advantage. The von Schweidler law’s free parameter lets it accommodate data, but accommodation is not explanation — it’s flexibility to fit things that aren’t real alongside things that are. The random barrier model’s predictions emerge directly from its theoretical structure: a distribution of barriers, thermally activated crossing, no tuning. When it fits better despite having less freedom to fit, the model is capturing genuine structure that the parameterized model is averaging over.

This is a specific instance of a general pattern: parameterless models that work are evidence of understanding. Models with free parameters that fit are evidence of flexibility. The distinction matters most when both fit well — the parameterless model is more likely to extrapolate correctly because its accuracy comes from structure, not adjustment.