Turbulence-induced dissipation-diffusion in fine-structures evolution is crucial for studying the energy translation process of nanoflare-loop large temporal–spatial turbulence magnetic reconnection. It is vital for resolving energy conversion between magnetic energy, acceleration energy (bulk kinetic energy), and heating energy (thermal kinetic energy) across different particle species (e.g., electron, ion, 3He, 4He, and other heavier particles) diffusion regions, which is key to understanding nanoflare heating and solar energetic particles' origin. As the first part of a two-paper series, in this study, we derived the explicit expression of turbulence-induced dissipation-diffusion terms under fully coupled hydrodynamics-magnetohydrodynamics-kinetic continuous scales by considering turbulence-resistance-induced self-organization and turbulence-viscosity-induced self-sustaining with filter theory. We enhanced the current relativistic hybrid particle-in-cell and lattice Boltzmann method by upgrading the input and dissipation-diffusion modules and adding a new turbulence-induced dissipation-diffusion module B. J. Zhu et al., Appl. Math. Model. 78, 932–967 (2020); B. J. Zhu et al., Earth Planet. Phys. 3, 17–25 (2019); B. J. Zhu et al., Appl. Math. Model. 78, 968–988 (2020); W. Wang and B. J. Zhu, “HIP-based heterogeneous parallel 3D LBM fluid simulator (HIP-LBM3D) V1.0 [software,” No. 2023SR0533996, 2023; B. J. Zhu et al., “Scalable simulations of 3D turbulence fine structure in nanoflare using a novel plasma statistical algorithm,” in Proceedings of the 5th International Conference on Statistics: Theory and Applications (ICSTA'23) (2023), p. 122; H. Yan et al., “A new fluid numerical RHPIC-LBM algorithm from statistical physics,” China patent 202311118994.2; W. Wang et al., “HIP-based heterogeneous parallel 3D LBM HD simulator (HIPHDLBM) V1.0 software,” No. 2023SR0533996, 2023; B. J. Zhu et al., “Software development of GeV-level-SEPs-induced extreme space weather disasters with plasma statistical physics theoretical model on domestic DCU accelerator heterogeneous supercomputer,” Prog. Rep. China Nucl. Sci. Technol.: Comput. Phys. 8, 1–40 (2024); Z. H. Fu et al., “A new ARM-based CPU implementation of the RHPIC-LBM code,” 32nd General Assembly Int. Union 197 (2024); W. Wang and B. J. Zhu, “HIP-based heterogeneous parallel 3D LBM MHD simulator (HIP-MHDLBM) V1.0 software,” No. 2024SR2094116, 2024; B. J. Zhu and W. Wang, “Dynamic-magnetohydrodynamic-kinetic coupled algorithm for RHPIC-LBM code,” China patent 202511005823.8 (2025); Z. K. Ma, “Fine-structure turbulence-induced dissipation-diffusion in the large temporal-spatial current sheet with mean field theory,” M.S. thesis, University of Chinese Academy of Sciences, 2025; Z. K. Ma et al., “Fine-structure investigation of the turbulence-induced dissipation-diffusion in Flare-CME current sheets,” Prog. Astron. 43(4), 1–26 (2025)]. Anomalous U-turbulence-induced viscosity dissipation-diffusion and B-turbulence-induced resistivity dissipation-diffusion, which exceed their classical counterparts, lead to self-generated turbulence through interactions and feedback between U and B, resulting in two fully coupled dissipation processes. The explicit expression and model are applied to explore the turbulence evolution of magnetic- and current-rotational instabilities in Part II B. J. Zhu et al., Phys. Fluid 37, 11 (2025).
zhu et al. (Sat,) studied this question.