First, I was looking for the . For the concentric spheres, the correct answer is that there is a simple equation. The reason there is, is that there are two types of points, outer sphere, and inner sphere. All points on the inner sphere can see only outer sphere points. So the system is governed by two simple equations for each bounce.
Inner sphere gets all energy from the outer sphere.
The exact values are based on the size of the spheres and the form factor from the inner sphere to a point on the outer sphere. Jacobi has an exact physical meaning. Each iteration of Jacobi propagates energy one more bounce into the environment. It also simplyfies using importance. Non iterative techniques are way too slow and require too much memory.