Accepted_test

The concepts being developed are based on conformation dynamics which is determined by rotations along dihedral angles around chemical bonds. The contribution of vibrations in the valence degrees of freedom is negligible and is not considered. The topology of the configuration space of a linear polymer is a multidimensional torus. The potential energy (PE) function is defined on a multidimensional torus and is represented as an expansion into a multidimensional Fourier series. The presence of identical or almost identical monomer units in a long polymer chain leads to the symmetry of the PE surface with respect to the permutation of the corresponding angular variables. This leads to the dependence of the expansion coefficients on the invariants of algebraic vectors of harmonic numbers, which makes it possible to model specific topographies of multidimensional energy surfaces and then the kinetic and thermodynamic effects. The movement of a representative point (RP) along the multidimensional surface of the PE is described by the equations of mechanics in a viscous medium. In liquid media (with a viscosity on the order of that of water), the inertial terms for atomic motions can be neglected. Using the methods of multidimensional geometry and taking into account the asymptotic properties of functions defined on multidimensional spheres, it is possible to establish a number of general patterns for the rules for RP motion on the multidimensional PE surface. The resulting rules for the RP motion are confirmed by the molecular dynamic simulations.