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 ($\mathcal{I}_\mathrm{BBH}$) - 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 derive $\mathcal{I}_\mathrm{BBH}$ for six astrophysically motivated population models describing dynamical and isolated formation channels. We find that $\mathcal{I}_\mathrm{BBH}$ offers a new criterion to probe the formation channels of LVK events with compact objects in the upper $(\gtrsim 60~M_\odot)$ and lower ($\lesssim 5~M_\odot$) mass-gaps. For GW190521, an event with both objects in the upper mass gap, $\mathcal{I}_\mathrm{BBH}$ distribution strongly favors second-generation mergers. For GW230529, a new event with the primary object in the lower mass gap, we note that $\mathcal{I}_\mathrm{BBH}$ mildly favors it with neutron star - black holes events. Our work provides a new framework to study the underlying demographics of compact binaries in the data-rich era of gravitational-wave astronomy.