State-of-the-art cosmological simulations of galaxies and galaxy clusters, such as IllustrisTNG (www.tng-project.org), suggest a scenario whereby the quenching of star formation in massive galaxies is caused by gas removal from the central regions of galaxies, in addition to gas heating, because of the activity of super massive black holes. The IllustrisTNG project comprises a series of large-volume cosmological simulations where gravity, magnetohydrodynamics and prescriptions for star formation, stellar evolution, metal enrichment, cooling and heating of the gas, galactic outflows and feedback from the supermassive black holes (SMBHs) are all taken into account within the LCDM paradigm. In practice, in these simulations, with one unique set of physical ingredients, we simultaneously resolve and model the inner structural details of thousands of galaxies across 5 orders of magnitude in stellar mass, across environments, and together with the evolution and dynamics of the inter-stellar, circum-galactic and inter-galactic media. The phenomena emerging from the underlying effective theory for galaxy formation include an observationally-consistent separation of star-forming and quenched galaxies across a wide range of observables across cosmic epochs. In this talk, I will focus on a specific, quantitative prediction by IllustrisTNG and its test against observational data. On the one hand, according to the IllustrisTNG simulations, star-forming and quiescent galaxies exhibit markedly distinct X-ray luminosity vs. K-band magnitude relations. In particular, the IllustrusTNG simulations predict a clear X-ray luminosity separation between star-forming and quiescent galaxies at M_K~ −24, corresponding to stellar masses of 10^10.5-10.7 solar masses, with star-forming galaxies being X-ray brighter than their quenched counterparts, by up to two orders of magnitudes (Truong, Pillepich et al. 2019). The difference is more prominent within the central regions (< Re) than at larger radii (<5Re) and it is qualitatively broadly consistent with currently available X-ray data of late and early-type galaxies in the local Universe. On the other hand, --if everything goes fine -- I will use data collected by eROSITA during the Science Verification phase and targeting galaxies from the Hyper Suprime Camera surveys with Subaru to perform more robust and extensive tests for the L_X dichotomy predicted insofar and hence to further probe the quenching mechanism in the Universe.