From Brownian motion formalism to fluctuation-induced force in a general fluctuating medium

TL;DR

This paper derives a rigorous microscopic framework for calculating fluctuation-induced forces between anisotropic materials mediated by a fluctuating medium, unifying different free energy concepts.

Contribution

It introduces a general formalism based on quantum Brownian motion to compute fluctuation-induced free energy between anisotropic objects at finite temperature.

Findings

Derived a rigorous partition function for anisotropic matter in a fluctuating medium.

Established the equivalence of induced-force, mean-force, and effective free energies.

Provided a general expression for fluctuation-induced free energy in the system.

Abstract

Starting from a microscopic approach and using the formalism of quantum Brownian motion, partition function of a system composed of two separated pieces of anisotropic matter and a fluctuating medium in finite temperature is obtained rigorously. A general expression for fluctuation-induced free energy between the separated anisotropic pieces of matter is obtained and it is shown that in the framework of induced-force, the free energy of mean-force and effective free energy are equivalent.