We study thermodynamic quantities and the stability of a black hole in a cavity using the Euclidean action formalism by Gibbons and Hawking based on the generalized uncertainty relation which is extended in a symmetric way with respect to the space and momentum without loss of generality. Two parameters in the uncertainty relation affect the thermodynamical quantities such as energy, entropy, and the heat capacity. In particular, it can be shown that the small black hole is unstable and it may decay either into a minimal black hole or a large black hole. We discuss a constraint for a large black hole comparable to the size of the cavity in connection with the critical mass.
The phenomenon of collective spontaneous annihilation of a magnetized electron-positron plasma is predicted. Like the superradiance in systems with discrete energy spectra, collective annihilation leads to the generation of powerful coherent radiation with the rate of this process considerably exceeding the spontaneous annihilation and collisional relaxation rates.