**5. Conclusion**

Dissipation consists of the irreversible transfer of energy from the proper MHD variables to the particle degrees of freedom of the plasma, considered as "microscopic" (and usually treated via Thermodynamics). Depending on the spatial and temporal scales on which dissipation takes place, it may activate some "sub-fluid level" of the theory, which interpolates between the continuous system, representing the traditional MHD, and the discrete one, describing the plasma through the motion of its particles. This "sub-fluid" level should probably consist of mesoscopic coherent structures existing because of dissipative process, and evolving through a stochastic (strongly noisy) dynamics. Consequently, the self-consistent theory describing this intermediate level of plasma description is expected to be a theory of SCSs.

In this Chapter, three models to approach this "SCS Theory" have been exposed: metriplectic algebrization of MHD, stochastic field theory and fractal magnetic reconnection.

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22.

Each of the three models tries to mimic one aspect of the complete theory of SCSs. The metriplectic MHD presents the non-Hamiltonian algebrization; the SFT for the resistive MHD is characterized by the presence of noise yielding a path integral approach; the fractal model of reconnection admits the irregular nature of MHD fields, involving the fractional calculus.

A large amount of work must still be done to imagine how those three approaches could be combined in a unique framework, the invoked "SCS Theory", reducing to the three models in different limits: this further research is for sure out of the subject of the work here, in which a flavour had to be given about some characteristics that this "SCS Theory" should have.

As a final remark, we underline that the self-consistent "SCS Theory" should present a sort of scale-covariance, because all the phenomena concerning plasma ISCs do involve multiscale dynamics. The technique of Renormalization Group will then be naturally applied to such a thory (see e.g. Chang et al., 1992 and references therein). A first direct application of such technique, using the exact full dynamic differential renormalization group for critical dynamics can be found in Chang et al. (1978). The use of Renormalization Group techniques to predict physical quantities to be compared with real spacecraft data is already well established (see e.g. Chang, 1999; Chang et al., 2004), and the results are very encouraging, confirming our idea that any "SCS Theory" has to be based on scale-covariance.
