Research Background:
Turbulence in nature refers to the complex, time-dependent, and spatially varying fluctuations that develop in fluids such as water, air, and plasma. It is a universal phenomenon that appears across a vast range of scales and systems—from atmospheric and oceanic currents on Earth, to interstellar gas in stars and galaxies, and even within jet engines and blood flow in human arteries. Turbulence is not merely chaotic; rather, it consists of an evolving hierarchy of interacting vortices, which may organize into large-scale structures or produce coherent flow patterns over time.
In nuclear fusion plasmas, turbulence plays a crucial role in regulating the confinement of thermal energy and the mixing of fuel particles, thereby directly impacting the performance of fusion reactors. Unlike simple fluid turbulence, plasma turbulence involves the simultaneous evolution of multiple physical fields, such as density, temperature, magnetic fields, and electric currents. These quantities are interwoven, forming a state where multiple flows and vortices are intricately entangled. Understanding and decoding the fundamental mechanisms of such complex, multi-field turbulence is essential for the control and optimization of future fusion reactors.
Traditionally, studies of plasma turbulence have focused on analyzing fluctuations of individual physical quantities. A standard method involves decomposing turbulence into a superposition of spatially uniform waves and then examining the distribution and transfer of fluctuation energy across scales. However, this wave-based decomposition becomes inadequate when the turbulence forms localized vortex structures or when multiple field quantities interact strongly. There has thus been a growing need for a new analysis framework—one that can capture localized structures and reveal the intertwined behavior of multiple fluctuating fields in a unified and physically meaningful way.
Research Results:
To investigate how vortices and flows emerge, localize, and interact within plasma turbulence, Go Yatomi of the National Institute for Fusion Science (a graduate student at SOKENDAI at the time of submission) and Associate Professor Motoki Nakata of Komazawa University (also a visiting researcher at RIKEN iTHEMS) have developed a novel analytical method called multi-field singular value decomposition (MFSVD). This technique extends the mathematical framework of singular value decomposition to multiple physical quantities, enabling the decomposition of complex turbulence into a set of common spatial patterns (or bases) that capture correlated fluctuations across different fields such as density, temperature, and electric potential.
MFSVD makes it possible to analyze how these multi-variable fluctuations collectively drive the formation and evolution of turbulent structures, such as vortices and large-scale flows, from a unified perspective. From the shared spatial modes extracted via MFSVD, the researchers further defined two new measures based on information entropy, concepts originally rooted in quantum mechanics and quantum information theory. The first is the von Neumann entropy (vNE), which quantifies the structural complexity and diversity of turbulent fluctuations. The second is entanglement entropy (EE), which measures the degree of coupling—or "entanglement"—between different turbulent structures, indicating how strongly they interact. Both quantities are derived from a mathematically constructed density matrix that parallels its counterpart in quantum theory, demonstrating a natural and powerful analogy between quantum states and turbulent systems.
By applying these information-theoretic quantities to numerical simulations of a plasma turbulence model, the research team identified a previously overlooked transition in turbulence states—one that cannot be detected through traditional energy-based analysis. This newly discovered transition reflects an abrupt shift in the collective patterns of vortices that occurs behind the scenes of major energy flows (Fig.1). Such pattern transitions can significantly influence macroscopic flow stability and are thus critical for understanding plasma confinement and transport processes.
Moreover, the entanglement entropy allowed the team to express detailed interactions, such as when and where specific patterns transfer energy or fluctuations to others, in a single measure. In conventional analysis, capturing such dynamics would require examining vast datasets. In contrast, these entropy-based quantities offer a new lens through which the essential features of nonlinear turbulent interactions can be distilled and studied efficiently.
Significance and Future Outlook:
The approach proposed in this study—analyzing turbulence transitions and interactions from the perspective of information entropy—holds promise not only for interpreting numerical simulation data but also for application to experimental measurements. Even in situations where only a limited number of sensors or diagnostic tools are available, this method can serve as a powerful guide to determine "how much measurement data is sufficient to capture essential turbulence features" and "which vortex structures should be prioritized for observation."
Importantly, the entropy-based framework developed here is not limited to plasma turbulence. It is expected to be applicable to a broad range of complex systems involving multi-scale flows and coupled fluctuations across many physical quantities—such as in atmospheric and oceanic sciences, traffic and transportation networks, and social systems. Looking ahead, the research team aims to deepen the theoretical correspondence between information entropy in turbulence and principles in quantum information theory, while also advancing the application of these methods to real-world measurement data. By combining the perspectives of both energy and information, this work opens a new avenue toward understanding the essential dynamics of turbulence and other complex phenomena.
