Entropy of open quantum systems and the Poisson distribution

The entropies of a harmonic oscillator and a quantum Klein–Gordon–Fock field with a static source are found in the coherent state. In both cases, the obtained expressions coincide up to a numerical factor with the Bekenstein–Hawking entropy for a black hole or, more precisely, for the physical vacuum around the hole. Such a coincidence and the property of a gravitational field to make a quantum system placed in this field decoherent lead to the assumption that the vacuum in the vicinity of a black hole is in a coherent state.