It gets a bit confusing tbh. In terms of light gathering the aperture is the aperture, so an f2.8 will gather the same amount of light in terms of exposure whether it be on m4/3, FF or whatever. What I mean by this is that if an exposure required ISO 200, f2.8 and 1/1000 on FF the same shot would require ISO 200, f2.8 and 1/1000 on m4/3 (I’ll not get into all the nuances of light transmission)
However it is the DOF that is different, and that is purely down to the crop factor and focal length. For example if you shot at 100mm f2.8 on FF, to get the same framing on m4/3 you would have to use a 50mm lens. Obviously DOF is related to the focal length of the lens (amongst other things) so if you’re shooting from the the same spot using a 50mm f2.8 lens it’s going to have a greater DOF than that shot with a 100mm f2.8 lens, does this make sense? If you wanted to ‘replicate’ the same DOF as 100 f2.8 on FF you’d have to use a 50mm f1.4 on m4/3. It‘s not exact, but near as dammit