Hydration Memory as a Classical Non-Markovian Effective Theory

This work develops a classical non-Markovian effective description of protein hydration using a generalized Langevin equation with a causal solvent-memory kernel. The framework is tested on 5 ns molecular-dynamics trajectories of ubiquitin and lysozyme.

A time-aggregated hydrogen-bond graph is disconnected in all tested configurations, so its Fiedler value cannot define a universal hydration timescale. A four-state temporal generator is numerically well defined, but Chapman–Kolmogorov tests reject a single Markov relaxation time for both proteins.

The robust output is instead given by residence statistics. For a 5 Å hydration shell, the inverse aggregate exit hazards are approximately 10.7 ps for ubiquitin and 11.1 ps for lysozyme, consistent with the corresponding restricted mean residence times. These values depend on the shell definition and coexist with broad residence-time distributions.

The results support a causal, multi-timescale and non-Markovian effective theory of protein hydration. The deposit includes the manuscript, analysis scripts, numerical results, figures, and reproducibility material.