A pr 2 00 1 THERMODYNAMICS OF COHERENT STATES AND BLACK HOLE ENTROPY

Mean values of any observable variable are always calculated in a coherent state as in a mixed state because the coherent state is an eigenstate of non-Hermitian operator. Thus, we propose the concept of a coherent ensemble closely resemble the canonical ensemble. The entropy and temperature are naturally defined for the coherent ensemble. 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 coincides with the effective temperature of a harmonic oscillator being in contact with a heath bath (Bloch formula) when the bath temperature tends to zero. The Bekenstein–Hawking entropy and temperature of a black hole can also be interpreted as an entropy and temperature of coherent states of a physical vacuum in the vicinity of a horizon surface.