Statistical Perturbation Calculus

Statistical Perturbation Calculus.—Statistical Mean Value. Let Q denote some physical quantity (electric polarization, magnetic polarization, exs,t%y), in general a function of the continuously varying canonic variables F (generalized momeita, generalized co-orclassical statistical mechanics, the mean value of Q is defined as ... 

The expansion of equation (100) is characteristic for classical statistical perturbation calculus. 

I now consider statement 3 How should an extension of dynamics be understood In the MPC theory the problem does not exist For the intrinsically stochastic systems there is no need for modifying the laws of dynamics. As for the LPS theory, one notes the presence of two essentially new concepts. The introduction of non-Hilbert functional spaces only concerns the definition of the states of the dynamical system, and not at all the law governing their evolution. It is an important precision introduced in statistical mechanics. The extension of dynamics thus only appears in the operation of regularization of the resonances. This step is also the one that is most difficult to justify rigorously it is related to the (practical) necessity to use perturbation calculus (see Appendix). 

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