To our knowledge, there is no generally accepted rigorous theory describing the spatio-temporal evolution of the sound energy density U Jm^-3 inside audio rooms.

However, the numerical statistical theory of Cairo techniques offers a rigorous theory based on PDE,

dU/dt)partial = α ∇^2 (U) + S

where U(x,y,z,t) is the sound energy density J m^-3 and α m^2 sec^-1 is the diffusivity of the sound energy.

In analogy with the heat diffusion PDE.