Context : Older models of Galactic chemical evolution ( GCE ) predict [ K/Fe ] ratios as much as 1 \mathrm { dex } lower than those inferred from stellar observations .
Abundances of potassium are mainly based on analyses of the 7698 \AA resonance line , and the discrepancy between GCE models and observations is in part caused by the assumption of local thermodynamic equilibrium ( LTE ) in spectroscopic analyses .

Aims : We study the statistical equilibrium of K I , focusing on the non-LTE effects on the 7698 \AA line .
We aim to determine how non-LTE abundances of potassium can improve the analysis of its chemical evolution , and help to constrain the yields of GCE models .

Methods : We construct a new model K I atom that employs the most up-to-date atomic data .
In particular , we calculate and present inelastic e+K collisional excitation cross-sections from the convergent close-coupling ( CCC ) and the B -Spline R -matrix ( BSR ) methods , and H+K collisions from the two-electron model ( LCAO ) .
We constructed a fine , extended grid of non-LTE abundance corrections based on 1D MARCS models that span 4000 < T _ { \mathrm { eff } } / K < 8000 , 0.50 < \log { g } < 5.00 , -5.00 < \mathrm { \left [ Fe / H \right ] } < +0.50 , and applied the corrections to potassium abundances extracted from the literature .

Results : In concordance with previous studies , we find severe non-LTE effects in the 7698 \AA line .
The line is stronger in non-LTE and the abundance corrections can reach \sim - 0.7 \mathrm { dex } for solar-metallicity stars such as Procyon .
We determine potassium abundances in six benchmark stars , and obtain consistent results from different optical lines .
We explore the effects of atmospheric inhomogeneity by computing for the first time a full 3D non-LTE stellar spectrum of K I lines for a test star .
We find that 3D modeling is necessary to predict a correct shape of the resonance 7698Ã line , but the line strength is similar to that found in 1D non-LTE .

Conclusions : Our non-LTE abundance corrections reduce the scatter and change the cosmic trends of literature potassium abundances .
In the regime [ Fe/H ] \lesssim - 1.0 the non-LTE abundances show a good agreement with the GCE model with yields from rotating massive stars .
The reduced scatter of the non-LTE corrected abundances of a sample of solar twins shows that line-by-line differential analysis techniques can not fully compensate for systematic LTE modelling errors ; the scatter introduced by such errors introduces a spurious dispersion to K evolution .