Forces exerted by a correlated fluid on embedded inclusions

TL;DR

This paper analyzes the forces exerted by a correlated fluid on embedded inclusions, clarifying the correct definition of these forces and their implications for Casimir-like interactions.

Contribution

It demonstrates that only the stress tensor-based definition accurately captures the medium's force on inclusions and explores differences in force variance.

Findings

Stress tensor definition yields correct medium-inclusion forces.

Thermal average of the force reproduces Casimir-like interactions.

Different force definitions lead to different force variance results.

Abstract

We investigate the forces exerted on embedded inclusions by a fluid medium with long-range correlations, described by an effective scalar field theory. Such forces are the basis for the medium-mediated Casimir-like force. To study these forces beyond thermal average, it is necessary to define them in each microstate of the medium. Two different definitions of these forces are currently used in the literature. We study the assumptions underlying them. We show that only the definition that uses the stress tensor of the medium gives the sought-after force exerted by the medium on an embedded inclusion. If a second inclusion is embedded in the medium, the thermal average of this force gives the usual Casimir-like force between the two inclusions. The other definition can be used in the different physical case of an object that interacts with the medium without being embedded in it. We show in a simple example that the two definitions yield different results for the variance of the Casimir-like force.