Thermodynamics of Coherent States and Black Hole Entropy

Abstract

Entropy and temperature of a system in a coherent state are naturally defined on a base of a density matrix of the system. As an example, entropy and temperature are evaluated for coherent states of a harmonic oscillator and quantum field described by the Klein--Gordon--Fock equation with a source term. It is shown, in particular, that the temperature of the coherent oscillator in a ground state coincides with the effective temperature of a harmonic oscillator being in contact with a heat bath (Bloch formula) when the bath temperature tends to zero. The Bekenstein--Hawking entropy of a black hole can also be interpreted as an entropy of coherent states of a physical vacuum in the vicinity of a horizon surface.