The discovery of dissipative collisions between two atomic nuclei opened a new field of research in nuclear physics. Before that, thermodynamic argumentation was infrequent and non-equilibrium statistical physics was absent in the scattering theory for atomic nuclei. The theory of nuclear physics was mainly written in terms of pure quantum states. The general acceptance of concepts such as friction and diffusion took some time because the textboak arguments for a statistical treatment seem not to be applicable. Neither is the number of partaking constituents very large nor is the identification of the microscopic variables evident, and the absence of a heat bath did not allow the use of conventional non-equilibrium physics where the response of the subsystem to small deviations from equilibrium is studied. Nevertheless, the highly incomplete experimental measurements clearly showed a dissipative behaviour in observables like energy, scattering angle, mass and charge number. The collected data resemble the actions observed in Brownian movement but the fluctuations are much larger then expected from Einstein's relation between friction and diffusion. As the study of Brownian movement is the key to the understanding of all dissipative phenomena, we use it to introduce the concepts which we then make use of in a specific dissipative model. We discuss the 'one-body dissipation model' in its richness of phenomena and compare 'its predictions to measured data. Special attention is paid to the non-equilibrium relation between friction (or mobility) and diffusion.