On the statistical symmetries of the Lundgren-Monin-Novikov hierarchy

The article by M. Waclawczyk et al. [Phys. Rev. E 90, 013022 (2014)] proposes two new statistical symmetries in the classical theory for turbulent hydrodynamic flows. In this Comment, however, we show that both symmetries are unphysical due to violating the principle of causality. In addition, they must get broken in order to be consistent with all physical constraints naturally arising in the statistical Lundgren-Monin-Novikov (LMN) description of turbulence. As a result, we state that besides the well-known classical symmetries of the LMN equations no new statistical symmetries exist. Finally, we criticize the relation between intermittency and global symmetries as it is presented throughout that study.