Generalized Ultra-relativistic High-Energy Non-Neutral Plasma Eigenmodes

We investigate the linear stability and electromagnetic eigenmode structure of a reduced thermodynamic dynamical system derived from the General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) [1-3]. A slow entropy-alignment variable is introduced to represent coarse-grained internal regulation of competing entropy production channels. Linearization about the thermodynamic balance manifold yields a minimal spectrum consisting of damped oscillatory mode pairs and a real entropy-alignment mode that controls slow evolution of transport properties. For a minimal field-moment realization, the frozen GENERIC operator produces a gyrotropic susceptibility tensor equivalent to the cold magnetized plasma dielectric response, recovering the standard Stix form and whistler dispersion in the frozen-regulation limit [4]. The imaginary and real parts of the GENERIC eigenvalues map directly to wave frequency and damping, respectively. Away from balance, the entropy-alignment dynamics introduce a slow dependence of the effective dissipation, implying exponential relaxation of wave attenuation on a thermodynamic timescale determined by the additional real eigenvalue. Parameter sweeps and root-locus analysis show that the dominant stability metric coincides with the physical growth rate and that the balance manifold defines a thermodynamic stability boundary. The results provide a thermodynamic reduction of kinetic plasma eigenmode dynamics that preserves standard wave limits while predicting slow regulation of damping and stability not captured by conventional linear plasma theory. Connections to ultra-magnetized and pair-plasma eigenmode literature are noted for context [5-7].