  We derive the Cardy--Verlinde entropy formula for the field theory that lives
on the boundary of an asymptotically de Sitter space with a black hole. The
boundary theory which is not conformal has a monotonic $C$--function defined by
the Casimir energy. The instability of the space due to Hawking radiation from
the black hole corresponds to an RG flow from the IR to the UV during which $C$
increases. The endpoint of black hole evaporation is de Sitter space which is
described by a conformal theory at the UV fixed point of the RG flow.
