  We show that, in warm inflation, the nearly constant Hubble rate and
temperature lead to an adiabatic evolution of the number density of particles
interacting with the thermal bath, even if thermal equilibrium cannot be
maintained. In this case, the number density is suppressed compared to the
equilibrium value but the associated phase-space distribution retains
approximately an equilibrium form, with a smaller amplitude and a slightly
smaller effective temperature. As an application, we explicitly construct a
baryogenesis mechanism during warm inflation based on the out-of-equilibrium
decay of particles in such an adiabatically evolving state. We show that this
generically leads to small baryon isocurvature perturbations, within the bounds
set by the Planck satellite. These are correlated with the main adiabatic
curvature perturbations but exhibit a distinct spectral index, which may
constitute a smoking gun for baryogenesis during warm inflation. Finally, we
discuss the prospects for other applications of adiabatically evolving
out-of-equilibrium states.
