Systems with mean-field like interactions display a short-time relaxation towards Quasi Stationary States (QSSs), whose lifetime increases with system size. Besides that, these states are "attractive", since one observes convergence towards
them from a different generic initial state. They are robust to external and stochastic perturbations and persist when a weak short-range interaction is added. Examples of systems where such states appear are: the Hamiltonian Mean-Field  (HMF) model, the free-electron laser,  wave-particle Hamiltonians, non neutral plasmas,  self-gravitating systems, 2D hydrodynamics. Recently, the use of Lynden-Bell entropy has been advocated to describe such states. In this talk, I will discuss the merits and drawbacks of this approach.

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