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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 itis a Ba\~nados-Teitelbom-Zanell$ (BTZ) spacetime and thus asymptotically AdS.The first law of thermodynamics applied to the thin shell, plus one equation ofstate for the shell's pressure and another for its temperature, leads to ashell's entropy, which is a function of its gravitational radius alone. Asimple example for this gravitational entropy, namely, a power law in thegravitational radius, is given. The equations of thermodynamic stability areanalyzed, resulting in certain allowed regions for the parameters entering theproblem. When the Hawking temperature is set on the shell and the shell ispushed up to its own gravitational radius, there is a finite quantumbackreaction that does not destroy the shell. One then finds that the entropyof the shell at the shell's gravitational radius is given by theBekenstein-Hawking entropy.

Entropy of thin shells in a (2+1)-dimensional asymptotically AdS spacetime and the BTZ black hole limit