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Pré-Publication, Document De Travail Année : 2023

Classical Density Functional Theory: The Local Density Approximation

Résumé

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.

Dates et versions

hal-04265172 , version 1 (30-10-2023)

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Michal Jex, Mathieu Lewin, Peter Madsen. Classical Density Functional Theory: The Local Density Approximation. 2023. ⟨hal-04265172⟩
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