Non-extensive visco-elastic theory .5. Diffusion equations, distribution functions viscosity and diffusion coefficients, correlation functions

This article is an important theoretical development of the previous articles (I) and (III) in which are introduced the basic concepts of the theory. Here, diffusion equations are established and their solutions are given for the simple model with one elastic constant and isotropy of reciprocal space. The classical diffusion laws for translation (Pick law) and rotation are recovered in the limit of very long times. The concepts of microscopic and macroscopic viscosity and self-diffusion coefficient are introduced. The difference between the two concepts vanishes above the transition. It is shown that the macroscopic viscosity and self-diffusion coefficient have a very steep variation with temperature below the transition. Tensorial order parameters are defined for rotation. Formal expressions for the time correlation functions of Legendre polynomials are established. These quantities allow to calculate the main correlations functions far analysis of dielectric relaxation, light scattering, and incoherent neutron scattering. All correlation functions, translational and rotational, are fundamentally non-exponential.