How Hot Is Radiation?

TL;DR

This paper introduces a rigorous method to define and analyze nonequilibrium radiation temperature, especially in laser radiation, demonstrating its dependence on intensity and frequency, and correcting common misconceptions.

Contribution

It develops a self-consistent framework for nonequilibrium radiation temperature using energy distribution over states, applicable to laser radiation and beyond.

Findings

High laser radiation temperatures depend on intensity and frequency.

Heuristic equilibrium-based temperatures are shown to be incorrect.

Conditions for valid nonequilibrium temperature definitions are established.

Abstract

A self-consistent approach to nonequilibrium radiation temperature is introduced using the distribution of the energy over states. We begin rigorously with ensembles of Hilbert spaces and end with practical examples based mainly on the far from equilibrium radiation of lasers. We show that very high, but not infinite, laser radiation temperatures depend on intensity and frequency. Heuristic "temperatures" derived from a misapplication of equilibrium arguments are shown to be incorrect. More general conditions for the validity of nonequilibrium temperatures are also established.