Are the black hole remnants produced from binary black hole mergers in GWTC-3 thermodynamically stable?

Black hole thermodynamics has brought strong hints of a profound and fundamental connection between gravity, thermodynamics, and quantum theory. If the black hole does behave like a natural thermodynamic system, it should be thermodynamically stable in a clean environment. In this paper, using the observational data of binary black hole (BBH) mergers observed by LIGO, Virgo, and KAGRA detectors, we check whether the black hole remnants produced from BBH mergers in the LIGO-Virgo-KAGRA catalog GWTC-3 are thermodynamically stable. The criterion for the thermodynamic stability is quite simple and is directly related to the black hole's spin, which states that a thermodynamically stable black hole remnant requires its dimensionless spin $a>a_* \simeq 0.68$. We check the posterior distributions of final spin $a_f$ for 83 black hole remnants in GWTC-3 and find the whole remnant population is consistent with the thermodynamically stable black hole with $99.98\%$ probability. This is the first verification of the thermodynamic stability of black hole remnants produced from BBH mergers.