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a potential would certainly lead to a spontaneous electron-positron pair production. In this process the negative-energy electrons from the Dirac sea (below the mass gap) would penetrate through the barrier and occupy a state in the upper continuum (above the mass gap) leaving a hole (positron) behind. But all electron states up to ϵ = µ are occupied (Fermi sea) to balance the bulk positive charge of protons. The situation is changed at finite temperatures when the particle-hole excitations are produced in the Fermi sea. Then, the electrons from the Dirac sea can occupy the vacancies in the Fermi sea. The process of thermal emission of electron-positron pairs from the sharp surface was considered earlier in ref. [20]. Here we want to point out other interesting processes, namely, the spontaneous 

