Noether's second theorem and covariant field theory of mechanical stresses in inhomogeneous ionic liquids

Petr E Brandyshev; Yury A Budkov

doi:10.1063/5.0148466

Noether's second theorem and covariant field theory of mechanical stresses in inhomogeneous ionic liquids

J Chem Phys. 2023 May 7;158(17):174114. doi: 10.1063/5.0148466.

Authors

Petr E Brandyshev¹, Yury A Budkov^{1

2}

Affiliations

¹ School of Applied Mathematics, HSE University, Tallinskaya st. 34, 123458 Moscow, Russia.
² G.A. Krestov Institute of Solution Chemistry of the Russian Academy of Sciences, Akademicheskaya st. 1, Ivanovo 153045, Russia.

PMID: 37144708
DOI: 10.1063/5.0148466

Abstract

In this paper, we present a covariant approach that utilizes Noether's second theorem to derive a symmetric stress tensor from the grand thermodynamic potential functional. We focus on the practical case where the density of the grand thermodynamic potential is dependent on the first and second coordinate derivatives of the scalar order parameters. Our approach is applied to several models of inhomogeneous ionic liquids that consider electrostatic correlations of ions or short-range correlations related to packing effects. Specifically, we derive analytical expressions for the symmetric stress tensors of the Cahn-Hilliard-like model, Bazant-Storey-Kornyshev model, and Maggs-Podgornik-Blossey model. All of these expressions are found to be consistent with respective self-consistent field equations.