We investigate whether open clusters (OCs) tend to energy equipartition, by means of direct N-body simulations with a broken power-law mass function. We find that the simulated OCs become strongly mass segregated, but the local velocity dispersion does not depend on the stellar mass for most of the mass range: the curve of the velocity dispersion as a function of mass is nearly flat even after several half-mass relaxation times, regardless of the adopted stellar evolution recipes and Galactic tidal field model. This result holds both if we start from virialized King models and if we use clumpy sub-virial initial conditions. The velocity dispersion of the most massive stars and stellar remnants tends to be higher than the velocity dispersion of the lighter stars. This trend is particularly evident in simulations without stellar evolution. We interpret this result as a consequence of the strong mass segregation, which leads to Spitzer's instability. Stellar winds delay the onset of the instability. Our simulations strongly support the result that OCs do not attain equipartition, for a wide range of initial conditions.

Resubmitted to MNRAS after implementing referee's comments