Classical maps are known as models with discrete time which enable one to explore a broad range of dynamics (from integrable to strongly chaotic). One famous example in the chaotic case is provided by the cat maps introduced by V. I. Arnold and A. A. Avez. It is a linear map on the two-dimensional torus. Recently a chain of coupled cat maps was introduced to model extremal black holes. We will remind the definition of the model and show how it can be used in a statistical physics perspective. We can define and exactly solve the diffusion problem and derive the diffusion coefficient from the microscopic dynamics. If time allows I will give some elements how to quantise the model.