Abstract
This thesis investigates the role of non-Gaussian thermostatting mechanisms in controlling structural and dynamical properties of supercooled Lennard--Jones liquids using molecular dynamics simulations. Conventional thermostats such as Nose--Hoover and Langevin enforce Maxwell--Boltzmann velocity statistics and therefore strictly sample canonical ensembles. In contrast, we introduce and analyze heavy-tailed stochastic thermostats that generate controlled deviations from Gaussian velocity distributions. The resulting non-equilibrium steady states exhibit enhanced velocity kurtosis, tunable through a heavy-tail parameter $\overline{A}$, which acts as a control knob for crystallization and dynamical arrest. By systematically varying thermostat noise statistics, polydispersity, and quench protocols, we quantify the impact of excess kurtosis $\kappa$ on bond-orientational order parameters, radial distribution functions $g(r)$, and intermediate scattering functions $F(q,t)$. We further show that heavy-tailed thermostatting modifies nucleation pathways and shifts the balance between crystallization and supercooling without altering the underlying pair interaction potential. A statistical-mechanical framework where effective inverse temperatures follow a Gamma distribution, provides a theoretical interpretation of the observed non-Gaussian velocity and provides a link between non-equilibrium statistics and relaxation slow-down in supercooled systems. These results establish non-Gaussian thermostatting as a principled method for engineering metastability and glass formation in model liquids, offering new insight into the interplay between microscopic velocity statistics and emergent structural order in MD systems.
Committee Chair
Zohar Nussinov
Committee Members
Alex Seidel; Erik Henriksen; Li Yang; Rohan Mishra
Degree
Doctor of Philosophy (PhD)
Author's Department
Physics
Document Type
Dissertation
Date of Award
4-22-2026
Language
English (en)
DOI
https://doi.org/10.7936/rnan-md87
Recommended Citation
Tsereteli, Giorgi, "Non-Gaussian Thermostatting and Heavy-Tailed Velocity Statistics in Supercooled Lennard–Jones Liquids" (2026). Arts & Sciences Graduate Student Theses and Dissertations. 3729.
The definitive version is available at https://doi.org/10.7936/rnan-md87