A non-Boltzmannian behavior of the energy distribution for quasi-stationary regimes of the Fermi-Pasta-Ulam β system

► New statistical properties of the Fermi-Pasta-Ulam beta system are found. ► The energy distribution of specific observables are studied: a deviation from the standard Boltzmann behavior is found. ► A q-exponential weight should be used instead. ► The classical exponential weight is restored in the large particle limit (mesoscopic nature of the phenomenon).