We recently derived, using the densityofstates approximation, analytic distribution functions for the outcomes of direct singlebinary scatterings. Using these outcome distribution functions, we present in this paper a selfconsistent statistical mechanicsbased analytic model obtained using the Fokker–Planck limit of the Boltzmann equation. Our model quantifies the dominant gravitational physics, combining both strong and weak single–binary interactions, which drives the time evolution of binary orbital parameter distributions in dense stellar environments. We focus in particular the distributions of binary orbital energies and eccentricities. We find a novel steadystate distribution of binary eccentricities, featuring strong depletions of both the highest and the lowest eccentricity binaries. In energy space, we compare the predictions of our analytic model to the results of numerical Nbody simulations, and find that the agreement is good for the initial conditions considered here. This work is a first step towards the development of a fully selfconsistent semianalytic model for dynamically evolving binary star populations in dense stellar environments due to direct fewbody interactions.
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ABSTRACT 
ABSTRACT As active galactic nuclei (AGN) ‘turn on’, some stars end up embedded in accretion discs around supermassive black holes (SMBHs) on retrograde orbits. Such stars experience strong headwinds, aerodynamic drag, ablation, and orbital evolution on short timescales. The loss of orbital angular momentum in the first ∼0.1 Myr of an AGN leads to a heavy rain of stars (‘starfall’) into the inner disc and on to the SMBH. A large AGN loss cone (θAGN, lc) can result from binary scatterings in the inner disc and yield tidal disruption events (TDEs). Signatures of starfall include optical/UV flares that rise in luminosity over time, particularly in the inner disc. If the SMBH mass is $M_{\rm SMBH} \gtrsim 10^{8}\, \mathrm{M}_{\odot }$, flares truncate abruptly and the star is swallowed. If $M_{\rm SMBH}\lt 10^{8}\, \mathrm{M}_{\odot }$, and if the infalling orbit lies within θAGN, lc, the flare is followed by a TDE that can be prograde or retrograde relative to the AGN inner disc. Retrograde AGN TDEs are overluminous and shortlived as inplane ejecta collide with the inner disc and a lower AGN state follows. Prograde AGN TDEs add angular momentum to inner disc gas and so start off looking like regular TDEs butmore »