  We demonstrate that baryonification algorithms, which displace particles in
gravity-only simulations according to physically-motivated prescriptions, can
simultaneously capture the impact of baryonic physics on the 2 and 3-point
statistics of matter. Specifically, we show that our implementation of a
baryonification algorithm jointly fits the changes induced by baryons on the
power spectrum and equilateral bispectrum on scales up to k < 5 h/Mpc and
redshifts z<2, as measured in six different cosmological hydrodynamical
simulations. The accuracy of our fits are typically 1% for the power spectrum,
and for the equilateral and squeezed bispectra, which somewhat degrades to 3%
for simulations with extreme feedback prescriptions. Our results support the
physical assumptions underlying baryonification approaches, and encourage their
use in interpreting weak gravitational lensing and other cosmological
observables.
