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Experimental particle spectra can be successfully described by power-lawtailed energy distributions characteristic to canonical equilibriumdistributions associated to R\'enyi's or Tsallis' entropy formula - over a widerange of energies, colliding system sizes, and produced hadron sorts. In orderto derive its evolution one needs a corresponding dynamical description of thesystem which results in such final state observables. The equations ofrelativistic fluid dynamics are obtained from a non-extensive Boltzmannequation consistent with Tsallis' non-extensive $q$-entropy formula. Thetransport coefficients like shear viscosity, bulk viscosity, and heatconductivity are evaluate based on a linearized collision integral.

Non-extensive statistics, relativistic kinetic theory and fluid dynamics