  Cold Dark Matter (CDM) simulations predict a central cusp in the mass
distribution of galaxies. This prediction is in stark contrast with
observations of dwarf galaxies which show a central plateau or 'core' in their
density distribution. The proposed solutions to this core-cusp problem can be
classified into two types. Either they invoke feedback mechanisms produced by
the baryonic component of the galaxies, or they assume the properties of the
dark matter (DM) particle to depart from the CDM hypothesis. Here we propose an
alternative yet complementary explanation. We argue that cores are unavoidable
in the self-gravitating systems of maximum entropy resulting from non-extensive
statistical mechanics. Their structure follows from the Tsallis entropy,
suitable for systems with long-range interactions. Strikingly, the mass density
profiles predicted by such thermodynamic equilibrium match the observed cores
without any adjustment or tuning. Thus, the principle of maximum Tsallis
entropy explains the presence of cores in dwarf galaxies.
