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Thermodynamic Potentials

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Thermodynamic potentials are state functions that are extremely useful in analyzing a thermodynamic system. They have dimensions of energy. The four important thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy. These thermodynamic potentials can be expressed using two of the following variables: pressure, volume, temperature, and entropy. These two variables are expressed as the rate of change of the thermodynamic potential with respect to other...

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Van der Waals Equation

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Potential energy or potential function plays an essential role in determining the stability of a mechanical system. If a system is subjected to both gravitational and elastic forces, the potential function of the system can be expressed as the algebraic sum of gravitational and elastic potential energy. If the system is in equilibrium and is displaced by a small amount, then the work done on the system equals the negative of the change in the system's potential energy from the initial to the...

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Updated: Jan 11, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

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Published on: April 8, 2020

Learned free-energy functionals from pair-correlation matching for dynamical density functional theory.

Karnik Ram^1,2, Jacobus Dijkman^3,4, René van Roij⁵

¹TU Munich, School of Computation, Information and Technology, Munich, Germany.

Physical Review. E

|November 18, 2025

Summary

This summary is machine-generated.

A learned neural free-energy functional for classical density functional theory (cDFT) can now be applied to dynamical density functional theory (DDFT) without retraining. This enables accurate simulations of complex colloidal systems and nonequilibrium dynamics.

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Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Published on: April 12, 2019

Area of Science:

Statistical mechanics
Computational physics
Colloidal science

Background:

Classical density functional theory (cDFT) and dynamical density functional theory (DDFT) model many-body colloidal systems.
Accurate excess free-energy functionals are crucial but often infeasible.
Prior work showed neural excess free-energy functionals can be learned for cDFT.

Purpose of the Study:

To apply a pre-learned neural excess free-energy functional to DDFT without retraining.
To simulate nonequilibrium overdamped dynamics of inhomogeneous densities using DDFT.
To develop and apply a gradient flow extension of DDFT for grand-canonical systems.

Main Methods:

Utilized a neural excess free-energy functional learned via pair-correlation matching.
Simulated three-dimensional Lennard-Jones systems with planar geometry under external potentials.
Extended DDFT using gradient flows for grand-canonical simulations.

Main Results:

Demonstrated successful application of the learned functional in DDFT for simulating dynamics.
Achieved good agreement between DDFT and Brownian dynamics simulations for inhomogeneous densities.
Showcased accurate simulations for gas adsorption systems using the extended DDFT.

Conclusions:

A learned free-energy functional can be effectively transferred to DDFT, eliminating the need for retraining.
This approach enables accurate and efficient modeling of complex many-body nonequilibrium systems.
The method shows promise for applications in areas like gas adsorption studies.