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 $$15\,\textrm{V}$$ 15 V collection-voltage dataset, the quadratic q ( T ) model is strongly preferred over the classical alternatives. For the $$0\,\textrm{V}$$ 0 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.