This study investigates the nonlinear evolution of tearing mode instabilities utilizing a quasiparticle framework integrated with spectral methods. By reformulating the resistive magnetohydrodynamic (MHD) equations via Galerkin spectral decomposition, a direct connection between MHD and quasiparticle statistics is established, where the wave-number–frequency relationship reflects the de Broglie duality ($p=\hslash k,\varepsilon =\hslash \omega$). Numerical simulations unveil three distinct stages: initial transient growth, a linear stage (${\gamma }_m\propto \left|m\right|$), and nonlinear evolution and saturation. Harmonic interactions display a growth mechanism governed by energy and momentum conservation (${\gamma }_m={\gamma }_{m^{\prime }}+{\gamma }_{m^{\prime \prime }},m=m^{\prime }+m^{\prime \prime }$). Statistical analysis indicates that the spectral energy distribution follows Maxwell-Boltzmann statistics, with the temperaturelike parameter $\beta$ evolving linearly during the linear stage. Comparisons with HL-2A experimental spectra validate the predictive capability of the model for the evolution of magnetic islands. This study bridges turbulence theory and statistical physics, offering a general mechanism for analyzing magnetic reconnection and nonlinear tearing mode instabilities in magnetized plasmas.

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• Magnetic reconnection
• Magnetohydrodynamics
• Nonlinear phenomena in plasmas
• Tearing instability