Thermodynamic and quantum fluctuations of horizon area

The event horizon is a source of irreversibility, analogous to statistical irreversibility. This is why for systems with an event horizon there is no difference between quantum and thermal fluctuations. Quantum processes of quantum tunneling determine the thermodynamics of these systems, their temperatures, entropies and fluctuations. We considered three examples of entropy variance that support this point of view: (i) the variance of the area of the black hole horizon, obtained by consideration of quantum fluctuations; (ii) the variance of the entropy of the Hubble volume in the de Sitter state, obtained by consideration of thermal fluctuations; and (iii) the variance of entropy in integers in the Planckon model, determined by the Poisson distribution.