Adiabatic means quasi-static and isoentropic - slow enough to create negligible amount of irreversible excitation. This is the common rationale of technically different definitions. E.g., Landau & Lifshic'es definition has two components - thermally isolated (to prevent entropy change by heat exchange) and slow (to prevent irreversible excitation). For a gaped quantum system adiabatic can by quite fast (just keep Planck constant times the characteristic driving rate below the value of the energy gap). 

To sum up, don't make "waves" entropy and you'll adiabatic.