The nature of the cross-scale connections between the inertial-range turbulent energy cascade and the small-scale kinetic processes in collisionless plasmas is explored through the analysis of two-dimensional hybrid Vlasov–Maxwell numerical simulation (HVM), with
particles, and through a proxy of the turbulent energy transfer rate, namely the local energy transfer (LET) rate. Correlations between pairs of variables, including those related to kinetic processes and to deviation from Maxwellian distributions, are first evidenced. Then, the general properties and the statistical scaling laws of the LET are described, confirming its reliability for the description of the turbulent cascade and revealing its textured topology. Finally, the connection between such proxy and the diagnostic variables is explored using conditional averaging, showing that several quantities are enhanced in the presence of large positive energy flux, and reduced near sites of negative flux. These observations can help in determining which processes are involved in the dissipation of energy at small scales, as for example the ion-cyclotron or mirror instabilities typically associated with perpendicular anisotropy of temperature.