History of the Kohlrausch (stretched exponential) function: Focus on uncited pioneering work in luminescence

TL;DR

This paper reviews the historical development of the Kohlrausch (stretched exponential) function, emphasizing overlooked pioneering works predating its common attribution to Kohlrausch, especially in luminescence studies.

Contribution

It uncovers and discusses previously uncited early research on the Kohlrausch function, highlighting its historical significance in non-equilibrium phenomena.

Findings

Identification of overlooked pioneering works from 101 years ago.

Clarification of the original context of the Kohlrausch function.

Enhanced understanding of the historical development of the stretched exponential model.

Abstract

The first use of the stretched exponential function to describe the time evolution of a non-equilibrium quantity is usually credited to Rudolph Kohlrausch (1809-1858), who in 1854 applied it to the discharge of a capacitor. Attention is drawn to a set of pioneering works on the Kohlrausch function, one of which published 101 years ago, and that are not mentioned by Cardona, Chamberlin, and Marx in Ann. Phys. (Leipzig) 16, 842 (2007).