The ubiquitous relativistic jet phenomena associated with black holes play a major role in high and very-high-energy (VHE) astrophysics. In particular, observations have demonstrated that blazars show VHE emission with time-variability from days (in the GeV band) to minutes (in the TeV band), implying very compact emission regions. The real mechanism able to explain the particle acceleration process responsible for this emission is still debated, but magnetic reconnection has been lately discussed as a strong potential candidate and, in some circumstances, as the only possible one. In this work, we present the results of three-dimensional special relativistic magnetohydrodynamic simulations of the development of reconnection events driven by turbulence induced by current-driven kink instability along a relativistic jet. We have performed a systematic identification of all reconnection regions in the system, characterizing their local magnetic field topology and quantifying the reconnection rates. We obtained average rates of $0.051pm0.026$ (in units of the Alfv{e}n speed) which are comparable to the predictions of the theory of turbulence-induced fast reconnection. Detailed statistical analysis also demonstrated that the fast reconnection events follow a log-normal distribution, which is a signature of its turbulent origin. To probe the robustness of our method, we have applied our results to the blazar Mrk 421. Building a synthetic light curve from the integrated power of the magnetic reconnection events, we evaluated the time-variability from a power spectral density analysis, obtaining a good agreement with the observations in the GeV band. This suggests that turbulent fast magnetic reconnection driven by kink instability can be a possible process behind the high energy emission variability phenomena observed in blazars.
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