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We present a comparison of the nitrogen-to-oxygen ratio (N/O) in 37 high-redshift galaxies at $z\sim$2 taken from the KMOS Lensed Emission Lines and VElocity Review (KLEVER) Survey with a comparison sample of local galaxies, taken from the Sloan Digital Sky Survey (SDSS). The KLEVER sample shows only a mild enrichment in N/O of $+$0.1 dex when compared to local galaxies at a given gas-phase metallicity (O/H), but shows a depletion in N/O of $-$0.36 dex when compared at a fixed stellar mass (M$_*$). We find a strong anti-correlation in local galaxies between N/O and SFR in the M$_*$-N/O plane, similar to the anti-correlation between O/H and SFR found in the mass-metallicity relation (MZR). We use this anti-correlation to construct a fundamental nitrogen relation (FNR), analogous to the fundamental metallicity relation (FMR). We find that KLEVER galaxies are consistent with both the FMR and the FNR. This suggests that the depletion of N/O in high-$z$ galaxies when considered at a fixed M$_*$ is driven by the redshift-evolution of the mass-metallicity relation in combination with a near redshift-invariant N/O-O/H relation. Furthermore, the existence of an fundamental nitrogen relation suggests that the mechanisms governing the fundamental metallicity relation must be probed by not only O/H, but also N/O, suggesting pure-pristine gas inflows are not the primary driver of the FMR, and other properties such as variations in galaxy age and star formation efficiency must be important.

We investigate the presence of ionised gas outflows in a sample of 141 main-sequence star-forming galaxies at $1.2 10.8$, AGN-dominated galaxies, suggesting that AGNs may be the primary drivers of these gas flows. Surprisingly, at $\log(M_\star/M_{\odot})\leq 9.6$, the observed line profiles are fully consistent with a rotating disc model, indicating that ionised gas outflows in dwarf galaxies might play a negligible role even during the peak of cosmic star-formation activity. Finally, we find that the observed mass loading factor scales with stellar mass as expected from the TNG50 cosmological simulation, but the ionised gas mass accounts for only 2$\%$ of the predicted value. This suggests that either the bulk of the outflowing mass is in other gaseous phases or the current feedback models implemented in cosmological simulations need to be revised., Comment: Accepted for publication in MNRAS, 28 pages, 20 figures