Application of Geometric Thermodynamics: \\ Analysis of High-Temperature Plasma as "Dynamic Condensed State" in Controlled Fusion

This work applies the unified framework of "Geometric Thermodynamics" – originally developed for black holes, cosmology, and quantum condensed matter – to the analysis of high-temperature plasma in magnetically confined controlled fusion. The framework's core is the universal decomposition of a system's information content into \textbf{structural information} $\mathcal{N}_{\text{struct}}$ (encoding static, ordered configurations) and \textbf{dynamic information} $\mathcal{N}_{\text{dyn}}$ (encoding excitations and disorder). We operationalize this framework for fusion plasma by defining $\mathcal{N}_{\text{struct}} \propto \xi_c$, the fraction of energy in coherent macroscopic structures (e.g., zonal flows, MHD modes), and $\mathcal{N}_{\text{dyn}} \propto \Sigma_{\text{turb}}$, the turbulent entropy production rate from microscopic fluctuations. This defines an information phase space $(\xi_c, \Sigma_{\text{turb}})$. We argue that a high-performance fusion plasma constitutes a \textbf{dynamic condensed state}, characterized by maximized $\mathcal{N}_{\text{struct}}$ ($\xi_c \rightarrow 1$) and minimized $\mathcal{N}_{\text{dyn}}$ ($\Sigma_{\text{turb}} \rightarrow 0$), analogous to ordered quantum states like superconductors. A set of coupled nonlinear evolution equations for $\xi_c$ and $\Sigma_{\text{turb}}$ is derived, from which the threshold condition for the Low-confinement (L-mode) to High-confinement (H-mode) transition is analytically obtained, explaining its power scaling. Furthermore, we propose a novel control paradigm: actively introducing topologically protected macroscopic structures (e.g., large-scale magnetic islands with net helicity) as "information seeds" to directly enhance $\xi_c$, thereby catalyzing the formation and stabilization of this dynamic condensed state with potentially lower external heating power. This perspective provides a unified conceptual and quantitative framework for understanding plasma confinement, turbulence suppression, and operational mode transitions, potentially informing new diagnostic metrics and control strategies for achieving robust fusion energy.