Statistical field theory of mechanical stresses in Coulomb fluids: beyond mean-field theory

P. E. Brandyshev, Yu. A. Budkov

Published 2023-06-13Version 1

In this paper, we introduce a statistical field theory that describes the macroscopic forces in inhomogeneous Coulomb fluids. Our approach employs a general covariant methodology, in conjunction with a functional Legendre transformation method, to calculate the stress tensor for Coulomb fluids. This tensor encompasses the mean-field stress tensor and the fluctuation corrections derived through the one-loop approximation. The correction for fluctuations includes a term that accounts for the thermal fluctuations of the local electrostatic potential and field in the vicinity of the mean-field configuration. This correlation stress tensor determines how electrostatic correlation affects the local stresses in a non-uniform Coulomb fluid. We would like to emphasize that our general approach is applicable not only to Coulomb fluids, but also to nonionic simple or complex fluids, for which the field-theoretic Hamiltonian is known as a functional of the relevant scalar order parameters.