Quantum-inspired information entropy in multifield turbulence

An information entropy for turbulence systems with multiple field quantities is formulated, as a new paradigm to explore the nonlinear dynamics and pattern formations. Combining quantum state descriptions in quantum mechanics into the turbulence field analysis, the von Neumann entropy (vNE) and the entanglement entropy (EE) are derived from a density matrix for the turbulence state in terms of the multifield singular value decomposition (MFSVD). Applying the information-theoretic entropy analyses to spatio-temporal dynamics in turbulent plasmas with phase-transition–like behavior, we discover a new nontrivial transition threshold regarding the vNE, which significantly deviates from the transition threshold of the field energy considered in the conventional approaches. These findings provide us with physically more diverse classifications of the turbulence state from the new perspective of “information”, in addition to the energetics of turbulent vortices. It is also revealed that the EE for nonlinear interactions in turbulence extracts the information regarding the strength of nonlinear mode couplings and the direction of net energy transfer. A plausible application of the EE to the turbulence measurements is demonstrated, as well as the associated reconstruction technique for fluctuation fields.