homogeneous and inhomogenous relaxation time

KFC

Consider two-level system, the relaxation time (T1) and the coherence relaxation time (T2). I wonder what's the relation between T1, T2 in homogeneous and inhomogeneous case?

Here is my thoughts. For inhomogeneous case, all atoms are behave independently, the 'random' phase relation will add up to lower the degree of coherence, hence, T2 will be smaller to that for homogeneous case, right?

If my statement is correct, T1 is same for bother inhomogeneous and homogeneous cases (right?). Hence, T1/T2 (inhomo.) > T1/T2 (homo) ???

And I remember (but not sure if it is correct), there is a relation between T1 and T2, says [tex]T1\geq 2T2[/tex]. How does this relation come from? Is that true for both homogeneous and inhomogeneous case? What does it imply physically if T1/T2 ?