Learned Free-Energy Functionals from Pair-Correlation Matching for Dynamical Density Functional Theory
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909881343148032 |
|---|---|
| author | Ram, Karnik Dijkman, Jacobus van Roij, René van de Meent, Jan-Willem Ensing, Bernd Welling, Max Cremers, Daniel |
| author_facet | Ram, Karnik Dijkman, Jacobus van Roij, René van de Meent, Jan-Willem Ensing, Bernd Welling, Max Cremers, Daniel |
| contents | Classical density functional theory (cDFT) and dynamical density functional theory (DDFT) are modern statistical mechanical theories for modeling many-body colloidal systems at the one-body density level. The theories hinge on knowing the excess free-energy accurately, which is however not feasible for most practical applications. Dijkman et al. [Phys. Rev. Lett. 134, 056103 (2025)] recently showed how a neural excess free-energy functional for cDFT can be learned from bulk simulations via pair-correlation matching. In this article, we demonstrate how this same functional can be applied to DDFT, without any retraining, to simulate non-equilibrium overdamped dynamics of inhomogeneous densities. We evaluate this on a 3D Lennard-Jones system with planar geometry under various complex external potentials and observe good agreement of the dynamical densities with those from expensive Brownian dynamic simulations, up to the limit of the adiabatic approximation. We further develop and apply an extension of DDFT based on gradient flows, to a grand-canonical system modeled after breakthrough gas adsorption studies, finding similarly good agreement. Our results demonstrate a practical route for leveraging learned free-energy functionals in DDFT, paving the way for accurate and efficient modeling of many-body non-equilibrium systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09543 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learned Free-Energy Functionals from Pair-Correlation Matching for Dynamical Density Functional Theory Ram, Karnik Dijkman, Jacobus van Roij, René van de Meent, Jan-Willem Ensing, Bernd Welling, Max Cremers, Daniel Soft Condensed Matter Statistical Mechanics Chemical Physics Classical density functional theory (cDFT) and dynamical density functional theory (DDFT) are modern statistical mechanical theories for modeling many-body colloidal systems at the one-body density level. The theories hinge on knowing the excess free-energy accurately, which is however not feasible for most practical applications. Dijkman et al. [Phys. Rev. Lett. 134, 056103 (2025)] recently showed how a neural excess free-energy functional for cDFT can be learned from bulk simulations via pair-correlation matching. In this article, we demonstrate how this same functional can be applied to DDFT, without any retraining, to simulate non-equilibrium overdamped dynamics of inhomogeneous densities. We evaluate this on a 3D Lennard-Jones system with planar geometry under various complex external potentials and observe good agreement of the dynamical densities with those from expensive Brownian dynamic simulations, up to the limit of the adiabatic approximation. We further develop and apply an extension of DDFT based on gradient flows, to a grand-canonical system modeled after breakthrough gas adsorption studies, finding similarly good agreement. Our results demonstrate a practical route for leveraging learned free-energy functionals in DDFT, paving the way for accurate and efficient modeling of many-body non-equilibrium systems. |
| title | Learned Free-Energy Functionals from Pair-Correlation Matching for Dynamical Density Functional Theory |
| topic | Soft Condensed Matter Statistical Mechanics Chemical Physics |
| url | https://arxiv.org/abs/2505.09543 |