  This paper analyses the turbulent energy cascade from the perspective of
statistical mechanics, and relates inter-scale energy fluxes to statistical
irreversibility and information-entropy production. The microscopical
reversibility of the energy cascade is tested by constructing a reversible 3D
turbulent system using a dynamic model for the sub-grid stresses. This system,
when reversed in time, develops a sustained inverse cascade towards the large
scales, evidencing that the characterisation of the inertial energy cascade
must consider the possibility of an inverse regime. This experiment is used to
study the origin of statistical irreversibility and the prevalence of direct
over inverse energy cascades in isotropic turbulence. Statistical
irreversibility, a property of statistical ensembles in phase space related to
entropy production, is connected to the dynamics of the energy cascade in
physical space by considering the space locality of the energy fluxes and their
relation to the local structure of the flow. A mechanism to explain the
probabilistic prevalence of direct energy transfer is proposed based the
dynamics of the rate-of-strain tensor, which is identified as the most
important source of statistical irreversibility in the energy cascade.
