  The thermodynamic equilibrium states of a static thin ring shell in a
(2+1)-dimensional spacetime with a negative cosmological constant are analyzed.
Inside the ring, the spacetime is pure anti-de Sitter (AdS), whereas outside it
is a Ba\~nados-Teitelbom-Zanell$ (BTZ) spacetime and thus asymptotically AdS.
The first law of thermodynamics applied to the thin shell, plus one equation of
state for the shell's pressure and another for its temperature, leads to a
shell's entropy, which is a function of its gravitational radius alone. A
simple example for this gravitational entropy, namely, a power law in the
gravitational radius, is given. The equations of thermodynamic stability are
analyzed, resulting in certain allowed regions for the parameters entering the
problem. When the Hawking temperature is set on the shell and the shell is
pushed up to its own gravitational radius, there is a finite quantum
backreaction that does not destroy the shell. One then finds that the entropy
of the shell at the shell's gravitational radius is given by the
Bekenstein-Hawking entropy.
