Markovian Form of Dynamic Equation

Now one can return to dynamic equation (3.4) of a macromolecule in very concentrated solutions and melts of polymers, which can be rewritten in the form 

Due to the preceding analysis, the extra forces of external and internal resistance Ff and Gf can be specified as 

In these formulae, is a friction coefficient of a particle in a monomer liquid, B and E are phenomenological parameters discussed in the previous sections, 

Expressions (3.32) and (3.33) are solutions of equations which are written below in the simplest covariant form (see Section 8.4 and Appendix D) 

The properties of the stochastic forces in the system of equations (3.31)-(3.35) are determined by the corresponding correlation functions which, usually (Chandrasekhar 1943), are found from the requirement that, at equilibrium, the set of equations must lead to well-known results. This condition leads to connection of the coefficients of friction with random-force correlation functions - the dissipation-fluctuation theorem. In the case under consideration, when matrixes f7 -7 and G 7 depend on the co-ordinates but not on the velocities of particles, the correlation functions of the stochastic forces in the system of equations (3.31) can be easily determined, according to the general rule (Diinweg 2003), as 

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