  We study the gravitational baryogenesis mechanism for generating baryon
asymmetry in the context of running vacuum models. Regardless if these models
can produce a viable cosmological evolution, we demonstrate that they produce a
non-zero baryon-to-entropy ratio even if the universe is filled with conformal
matter. This is a sound difference between the running vacuum gravitational
baryogenesis and the Einstein-Hilbert one, since in the latter case, the
predicted baryon-to-entropy ratio is zero. We consider two well known and most
used running vacuum models and show that the resulting baryon-to-entropy ratio
is compatible with the observational data. Moreover, we also show that the
mechanism of gravitational baryogenesis may constrain the running vacuum
models.

General Relativity and Quantum Cosmology;Cosmology and Nongalactic Astrophysics