A mechanical derivation of the evolution equation for scintillating crystals: Recombination–diffusion–drift equations, gradient flows and Wasserstein measures

In a series of previous papers we obtained, by the means of the mechanics of continua with microstructure, the Reaction–Diffusion–Drift equation which describes the evolution of charge carriers in scintillators. Here we deal, first of all, with the consequences of constitutive assumptions for the entropic and dissipative terms. In the case of Boltzmann–Gibbs entropy, we show that the equation admits a gradient flows structure: moreover, we show that the drift–diffusion part is a Wasserstein gradient flow and we show how the energy dissipation is correlated with an appropriate Wasserstein distance.