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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.

On the basis of numerical solution to the Maxwell-Bloch equations within an one-dimensional two-level model of a superradiant laser with a symmetric cavity where a photon lifetime is less than an incoherent relaxation time of the optical dipole oscillations of active centers, we find that a spontaneous asymmetric generation of the counter-propagating waves is possible under a continuous homogeneous pumping of an active medium. We show that such a phenomenon of a symmetry breaking of the spatial profiles of the counter-propagating waves of an electromagnetic field as well as the polarization and population inversion of an active medium in the considered case of a weak inhomogeneous broadening of an operating transition is caused by an asymmetric half-wavelength nonlinear grating of the population inversion of the transition’s energy levels which is produced by these waves.