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https://stockholmuniversity.zoom.us/j/622224375
Meeting ID: 622 224 375
Abstract:
When the complete understanding of a complex system is not available, as, e.g., for systems considered in the real world, we need a top-down approach to complexity. In this approach, one may desire to understand general multipoint statistics. Here, such a general approach is presented and discussed based on examples from turbulence and sea waves. Our main idea is based on the cascade picture of turbulence, entangling fluctuations from large to small scales. Inspired by this cascade picture, we express the general multipoint statistics by the statistics of scale-dependent fluctuations of variables and relate it to a scale-dependent process, which finally is a stochastic cascade process. We show how to extract from empirical data a Fokker–Planck equation for this cascade process which allows the generation of surrogate data to forecast extreme events.
Knowing a comprehensive stochastic description of a complex system in terms of Fokker-Planck equations, this allows to develop a nonequilibrium thermodynamics for the complex systems. Although classical macroscopic systems are considered modern results discovered fro micro systems like the fluctuation theorems can be applied. In particular to each local structure of the complex system entropy values can be allocated. These entropies accurately fulfill a rigorous law, namely the integral fluctuations theorem. Most interestingly these entropies can be used to select special structures. Thus extreme events, like rogue waves are marked my negative entropy values. For turbulence we see that negative entropy leads to jumps in the velocity field.
To analyse data there is an open source software package under: github.com/andre-fuchs-uni-oldenburg/ OPEN_FPE_IFT
Reference:
Phys. Rev. F 5, 034602 (2020)
Annu. Rev. Condens. Matter Phys. 2019.