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Temporal discontinuity in the permittivity of a nondispersive dielectric (temporal boundary) is a conventional model for considering electromagnetic phenomena in dynamic materials and metamaterials. Here we apply a more general model of a Lorentz medium with the rapidly changing density of its structural elements (oscillators) or their resonant frequency to determine the realms of applicability of the conventional temporal boundary model. We demonstrate the dependence of the continuity conditions and the energy relations at a temporal boundary on the nonstationarity mechanism and the ratio between the rate of nonstationarity and the characteristic frequencies in the system.

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For surface plasmons on graphene in an arbitrary dielectric environment, combinations of the plasmon energy and frequency (adiabatic invariants) that are conserved during slow time-variations of the graphene free carrier density are obtained. The invariants allow one to find the plasmon energy changes directly from the frequency shift without solving a dynamic equation. The invariants have a different form in the cases of increasing and decreasing carrier density. In both cases, however, they predict that plasmon frequency shifting is accompanied by a decrease of the plasmon energy.