Does the nonlinear statistics ( power law, long- range interactions cases for example ) can be locally aproximated with linear statistics ( LSM, Gaussian case) , i.e. ( linear regression, short range interactions) from the case of partial information ( Tsallis entropy, partial information, fuzzy entropy) to the case of Shannon entropy, total information, with control systems method ( sensors, actuators ).
In the case of linear thermodynamics, the solutions must be optimized with the Jaynes method, but for nonlinear thermodynamics we must use the fuzzy entropy and appropriate methods.
I am interested to know, does this approach can be applied on controlled nuclear fusion ( deuterium-tritium reactions ). Namely, we have nonlinear stochastic Vlasov Poisson Fokker Planck equation ( long term distance, Coulomb forces, ions, electrons ) and nonlinear polynomial regression that after linearization could be approximated locally with linearized Boltzmann equations ( neutrons n, short term distance, linear regression) and then ,according to the formula D+T=He+n+E, we obtain optimal stabilization via neutron spectrometers .
Experiments with nonlinear regression should ensure the optimal growth and trend of cummulative entropy at instabilities case too. It can be used for the simulation of experiments also.
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