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arXiv · 2310.18028

Classical Density Functional Theory: The Local Density Approximation

Michal Jex·Mathieu Lewin·Peter Madsen
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Abstract

We prove that the lowest free energy of a classical interacting system at temperature $T$ with a prescribed density profile $\rho(x)$ can be approximated by the local free energy $\int f_T(\rho(x))dx$, provided that $\rho$ varies slowly over sufficiently large length scales. A quantitative error on the difference is provided in terms of the gradient of the density. Here $f_T$ is the free energy per unit volume of an infinite homogeneous gas of the corresponding uniform density. The proof uses quantitative Ruelle bounds (estimates on the local number of particles in a large system), which are derived in an appendix.

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Michal Jex, Mathieu Lewin, Peter Madsen. 2023-10-27. Classical Density Functional Theory: The Local Density Approximation. https://doi.org/10.1142/s0129055x24500375

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