Non-equilibrium Statistical Properties, Path-dependent Information Geometry, and Entropy Relations in Edge-Localized Modes in Fusion Plasmas

We investigate time-varying turbulence statistical properties of edge-localized modes (ELMs) in fusion plasmas. By utilizing a simplified stochastic model, we calculate a time-dependent probability density function and various entropy-related quantities such as entropy, entropy production, entropy flux, mutual information, and information flow and path-dependent information geometry. A thorough analysis is performed to elucidate the effects on ELM dynamics (evolution, suppression, mitigation, etc.) of different values of stochastic noise and different forms of a time-varying input power. Furthermore, the time-irreversibility and hysteresis are investigated through the employment of forward and back processes where a time-varying input power varies mirror-symmetrically in time. Among all the statistical quantities, the path-dependent information geometry is shown to be a robust diagnostic for quantifying hysteresis and self-regulation as well as for an early detection of subtle changes in ELM dynamics, for example, caused by a sudden change in the input power.