Merging of stellar-mass binary black holes (BBHs) could take place within the accretion disks of active galactic nuclei (AGN). The resulting BH remnant is likely to accrete the disk gas at a super-Eddington rate, launching a fast, quasi-spherical outflow (wind). Particles will be accelerated by shocks driven by the wind, subsequently interacting with the shocked disk gas or radiation field through hadronic processes and resulting in the production of high-energy neutrinos and potential electromagnetic (EM) emission. This study delves into the intricate evolution of the shock driven by a merged BH wind within an AGN disk. Subsequently, we calculated the production of neutrinos and the expected detection numbers for a single event, along with their contributions to the overall diffuse neutrino background. Our analysis, which considers various scenarios, reveals considerable neutrino production and possible detection by IceCube for nearby events. The contribution of merged BH winds on the diffuse neutrino background is minor due to the low event rate density, but it can be improved to some extent for some optimistic parameters. We also propose that there could be two neutrino/EM bursts, one originating from the premerger BBH wind and the other from the merged BH wind, with the latter typically having a delay to the gravitational wave (GW) event of around tens of days. When combined with the anticipated GWs emitted during the BBH merger, such a system emerges as a promising candidate for joint observations involving neutrinos, GWs, and EM signals.
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