  A static self-gravitating electrically charged spherical thin shell embedded
in a (3+1)-dimensional spacetime is used to study the thermodynamic and
entropic properties of the corresponding spacetime. Inside the shell, the
spacetime is flat, outside it is Reissner-Nordstr\"om, and this establishes the
energy density, the pressure, and the electric charge in the shell. Imposing
that the shell is at a given local temperature and that the first law of
thermodynamics holds on the shell one can find the integrability conditions for
the temperature and for the thermodynamic electric potential, the thermodynamic
equilibrium states, and the thermodynamic stability conditions. Through the
integrability conditions and the first law of thermodynamics an expression for
the shell's entropy can be calculated. It is found that the shell's entropy is
a function of the shell's gravitational and Cauchy radii alone. A plethora of
sets of temperature and electric potential equations of state can be given. One
set of equations of state is related to the Hawking temperature and a precisely
given electric potential. Then, as one pushes the shell to its own
gravitational radius and the temperature is set precisely equal to the Hawking
temperature, so that there is a finite quantum backreaction, one finds that the
entropy of the shell equals the Bekenstein-Hawking entropy for a black hole.
Other set of equations of state are given and the thermodynamic properties
analyzed. Whatever the initial equation of state for the temperature, as the
shell radius approaches its own gravitational radius, the quantum backreaction
imposes the Hawking temperature for the shell in this limit. Thus, when the
shell's radius is sent to the shell's own gravitational radius the formalism
developed allows to find the precise form of the Bekenstein-Hawking entropy of
the correlated black hole.
