# Radiative heat transfer and nonequilibrium Casimir-Lifshitz force in many-body systems with planar geometry

## TL;DR

This paper develops a comprehensive theoretical framework combining scattering theory and fluctuational electrodynamics to analyze photon-mediated energy and momentum transfer in many-body planar systems out of thermal equilibrium, including Casimir-Lifshitz forces.

## Contribution

It introduces explicit formulas for energy and momentum transfer coefficients in N-body systems, extending the analysis to non-equilibrium conditions and multi-body interactions.

## Key findings

- Derived explicit formulas for energy transmission coefficients.
- Formulated methods to calculate local equilibrium temperatures.
- Demonstrated the impact of additional slabs on heat transfer and forces in three-body systems.

## Abstract

A general theory of photon-mediated energy and momentum transfer in N-body planar systems out of thermal equilibrium is introduced. It is based on the combination of the scattering theory and the fluctuational-electrodynamics approach in many-body systems. By making a Landauer-like formulation of the heat transfer problem, explicit formulas for the energy transmission coefficients between two distinct slabs as well as the self-coupling coefficients are derived and expressed in terms of the reflection and transmission coefficients of the single bodies. We also show how to calculate local equilibrium temperatures in such systems. An analogous formulation is introduced to quantify momentum transfer coefficients describing Casimir-Lifshitz forces out of thermal equilibrium. Forces at thermal equilibrium are readily obtained as a particular case. As an illustration of this general theoretical framework, we show on three-body systems how the presence of a fourth slab can impact equilibrium temperatures in heat-transfer problems and equilibrium positions resulting from the forces acting on the system.