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This paper analyses the turbulent energy cascade from the perspective ofstatistical mechanics, and relates inter-scale energy fluxes to statisticalirreversibility and information-entropy production. The microscopicalreversibility of the energy cascade is tested by constructing a reversible 3Dturbulent system using a dynamic model for the sub-grid stresses. This system,when reversed in time, develops a sustained inverse cascade towards the largescales, evidencing that the characterisation of the inertial energy cascademust consider the possibility of an inverse regime. This experiment is used tostudy the origin of statistical irreversibility and the prevalence of directover inverse energy cascades in isotropic turbulence. Statisticalirreversibility, a property of statistical ensembles in phase space related toentropy production, is connected to the dynamics of the energy cascade inphysical space by considering the space locality of the energy fluxes and theirrelation to the local structure of the flow. A mechanism to explain theprobabilistic prevalence of direct energy transfer is proposed based thedynamics of the rate-of-strain tensor, which is identified as the mostimportant source of statistical irreversibility in the energy cascade.

Entropy, irreversibility and cascades in the inertial range of isotropic turbulence