Thermionic emission in nonequilibrium states: an application to carbon nanotubes

Abstract

We test a phenomenological extension of the Richardson–Dushman equation for thermionic emission based on Tsallis’ nonextensive statistics. A temperature-dependent effective entropic index is represented by a polynomial centered on the observed temperature interval, and its parameters are inferred from two datasets for self–Joule–heated individual carbon nanotubes. To avoid comparing a flexible nonlinear model with an artificially restrictive baseline, we analyze seven alternatives: Richardson–Dushman emission with a free effective prefactor, a one-dimensional thermionic law, a free temperature exponent, a temperature-dependent work function, and nonextensive models with constant, linear, and quadratic q(T). Identical broad bounded uniform priors and nested sampling are used for both samples to obtain posterior distributions, Bayesian evidences, and information criteria. For the \(15\,\textrm{V}\) collection-voltage dataset, the quadratic q(T) model is strongly preferred over the classical alternatives. For the \(0\,\textrm{V}\) dataset, quadratic q(T) also ranks first, although its evidence and BIC differences relative to the temperature-dependent work function model are inconclusive. Thus, the data support temperature-dependent corrections to ideal thermionic emission, but do not establish a unique nonextensive interpretation across both configurations.