  The irreversible turbulent energy cascade epitomizes strongly non-equilibrium
systems. At the level of single fluid particles, time irreversibility is
revealed by the asymmetry of the rate of kinetic energy change, the Lagrangian
power, whose moments display a power-law dependence on the Reynolds number, as
recently shown by Xu et al. [H. Xu et al, Proc. Natl. Acad. Sci. U.S.A. 111,
7558 (2014)]. Here Lagrangian power statistics are rationalized within the
multifractal model of turbulence, whose predictions are shown to agree with
numerical and empirical data. Multifractal predictions are also tested, for
very large Reynolds numbers, in dynamical models of the turbulent cascade,
obtaining remarkably good agreement for statistical quantities insensitive to
the asymmetry and, remarkably, deviations for those probing the asymmetry.
These findings raise fundamental questions concerning time irreversibility in
the infinite-Reynolds-number limit of the Navier-Stokes equations.
