Information approach, noncanonical

In this section we plan to discuss the dynamic versus the thermodynamic approach to noncanonical equilibrium. We plan to show that the thermodynamic method, in the form of an information approach, does not yield satisfactory result. The dynamic approach is more promising than the information approach, even if it involves difficult conceptual problems that have not yet been solved. We argue, however, that the strange response of fluctuations with inverse power law correlation to perturbation, illustrated in Section VII, might turn out to be useful in settling these difficult conceptual problems. 

From one point of view, (109) can be interpreted as a manifestation of the noncanonical nature of the microscopic equation of motion and supports the idea of dissipative effects on the microscopic level (for time scale t < t/). From another point of view (109) can be related to the coarse graining of the phase volume minimum cells. The concept of fractional evolution is due to the action of the averaging operator [45]. Each application of the averaging operator is equivalent to a loss of information regarding the short time mobility and is closely associated with the renormalization approach ideas [239]. 

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