Proof of Non-invariance of Magnetic Helicity in Ideal Plasmas and a General Theory of Self-organization for Open and Dissipative Dynamical Systems

"It is proved that the magnetic helicity is not invariant, even in an ideal plasma. A novel general theory is presented in which a variety of self-organized states in open and dissipative dynamical systems with various fluctuations can be found. This theory is based on the principle that the self-organized states must be those states for which the rate of change of global autocorrelations for multiple dynamical field quantities, which depend on multidimensional mutually independent variables, is minimized. One of the important points of this theory is that the original generalized dynamic equations are embedded in the final equivalent definition for the self-organized states, and therefore the equations deduced from the final equivalent definition include all the time evolution characteristics of the dynamical system of interest. Since states derived from the Euler-Lagrange equations with the use of variational calculus have minimal rates of change of the global autocorrelations, they are most stable and unchangeable compared with other states.