# Energy flux of electromagnetic field in stochastic model of radiative heat transfer in dielectric solid medium

## TL;DR

This paper develops a stochastic model for radiative heat transfer in dielectric solids, incorporating electromagnetic fluctuations due to thermal atom fluctuations, and calculates the energy flux density based on temperature distribution.

## Contribution

It introduces a novel stochastic framework using Ornstein-Uhlenbeck processes to model electromagnetic fluctuations in dielectric media for heat transfer analysis.

## Key findings

- Derived an expression for electromagnetic energy flux density as a functional of temperature.
- Established a stochastic model linking thermal fluctuations to electromagnetic heat transfer.
- Provided a mathematical basis for analyzing radiative heat transfer in dielectric solids.

## Abstract

The stochastic model that describes radiative heat transfer in dielectric medium is built. The model is based on the representation that heat transfer is realized both by heat conductivity mechanism in it and due to the electromagnetic radiation that is generated by thermal fluctuations of atoms in the medium. Using the fluctuation-dissipative theorem, on the basis of such physical suppositions, the stochastic model is formulated in the form of the infinite dimensional Ornstein-Uhlenbeck process that describes medium fluctuations. In the model frameworks, the energy flux density of fluctuating electromagnetic field is calculated in the form of the functional of temperature distribution in three-dimensional medium sample.