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Supermassive black holes (SMBHs) which reside at the centres of galaxies caninject vast amounts of energy into the surrounding gas and are thought to be aviable mechanism to quench star-formation in massive galaxies. Here we studythe $10^{9\textrm{--}12.5}\,\mathrm{M_\odot}$ stellar mass central galaxypopulation of the IllustrisTNG simulation, specifically the TNG100 and TNG300volumes at \zeq{0}, and show how the three components -- SMBH, galaxy, andcircumgalactic medium (CGM) -- are interconnected in their evolution. We findthat gas entropy is a sensitive diagnostic of feedback injection. Inparticular, we demonstrate how the onset of the low-accretion BH feedback mode,realised in the IllustrisTNG model as a kinetic, BH-driven wind, leads not onlyto star-formation quenching at stellar masses$\gtrsim10^{10.5}\mathrm{M_\odot}$ but also to a change in thermodynamicproperties of the (\emph{non}-star-forming) gas, both within the galaxy andbeyond. The IllustrisTNG kinetic feedback from SMBHs increases the average gasentropy, within the galaxy and in the CGM, lengthening typical gas coolingtimes from $10\textrm{--}100\,\mathrm{Myr}$ to $1\textrm{--}10\,\mathrm{Gyr}$,effectively ceasing ongoing star-formation and inhibiting radiative cooling andfuture gas accretion. In practice, the same AGN feedback channel issimultaneously `ejective' and `preventative' and leaves an imprint on thetemperature, density, entropy, and cooling times also in the outer reaches ofthe gas halo, up to distances of several hundred kiloparsecs. In theIllustrisTNG model, a long-lasting quenching state can occur for aheterogeneous CGM, whereby the hot and dilute CGM gas of quiescent galaxiescontains regions of low-entropy gas with short cooling times.

Ejective and preventative: the IllustrisTNG black hole feedback and its effects on the thermodynamics of the gas within and around galaxies