  We reconsider the interrelation between the Schwarzschild radius and mass of
a spherical symmetric non-rotating and uncharged black hole. By applying the
relativistic mass-energy equivalence, the area of the horizon is expressed
independently of the Schwarzschild radius in terms of an occupation number
operator corresponding to the underlying many-body system of the particles
inside the black hole. Given the expectation value of the area, the von Neumann
entropy based on the matter or radiation inside the black hole is maximized to
obtain the equilibrium probability density operator of the underlying ensemble.
We apply this approach to an ideal gas of ultra-relativistic particles and to
particles of rest mass zero. For both, the entropy is expressed in terms of the
horizon area of the black hole. In addition, the quantum fluctuations inside
the black hole are expressed in terms of the standard deviation of the horizon
area. The thermodynamic concept is finalized by a generalized Planck law of the
surface area which is derived at the end.
