Principle of second maximum entropy and Reynolds equations in stohastic dynamics of one dimension nonlinear systems

The new approach to deriving of averaging dynamics of finite-dimension nonlinear systems on a base of variational principle of maximum entropy are represented in thid work. The variatioanl principle are formulated using the method of conjugate function. The derivation of nonlinear systems in avaraging constructs on a base of general approach known as a Reynolds theory which widly applaied in turbulencr theory. In work the problem of point dynamics in potential force field of general form are represented. The equations closed derivation of dynnamics in averaging are intriduced. As was shown this equations allowed the conservation law of specific entropy and such theory are the Hamilton theory in reference to fuul specific entropy.