Nonequilibrium Stefan-Boltzmann law

TL;DR

This paper generalizes the classical Stefan-Boltzmann law to nonequilibrium conditions, demonstrating that the energy current between two bodies at different temperatures follows a similar fourth-power temperature difference law.

Contribution

It introduces a nonequilibrium Stefan-Boltzmann law describing energy transfer between bodies at different temperatures, extending classical equilibrium radiation laws.

Findings

Energy current follows a Stefan-Boltzmann-like law.

System reaches a stationary state with a temperature-dependent energy flux.

Classical laws are extended to nonequilibrium thermal radiation.

Abstract

We study thermal radiation outside equilibrium. The situation considered consists of two bodies emitting photons at two different temperatures. We show that the system evolves to a stationary state characterized by an energy current which satisfies a Stefan-Boltzmann-like law expressing it as the difference of the temperatures to the fourth power of the emitters . The results obtained show how the classical laws governing the thermal radiation at equlibrium can be generalized away from equilibrium situations.