Distinguishing the Demographics of Compact Binaries with Merger Entropy Index

The coalescence of binary black holes and neutron stars increases the entropy in the universe. The release of entropy from the inspiral stage to the merger depends primarily on the mass and spin vectors of the compact binary. In this study, we report a novel application of entropy to study the demographics of the compact binaries reported by the LIGO-Virgo-KAGRA (LVK) Collaboration. We compute an astrophysical distribution of the Merger Entropy Index (Ι_BBH) - a mass-independent measure of the efficiency of entropy transfer for black hole binaries - for all the events reported in the LVK Gravitational-Wave Transient Catalogs. We compare this distribution with that from dynamic and isolated formation channels. We find that Ι_BBH offers a new criterion to distinguish formation channels for binaries with compact objects in the upper (> 60M_☉) and lower (< 5M_☉) mass-gaps. For GW230529, a new event with compact object in the lower mass-gap, we note that Ι_BBH distribution 61% statistical similarity with that of confirmed neutron star-black hole merger events. For GW190521, an event with both objects in the upper mass-gap, Ι_BBH distribution has 91% statistical similarity with that of the second generation mergers. Our work provides a new framework to study the underlying demographics of compact binaries in the data-rich era of gravitational-wave astronomy.