Relationship between Energy of Motion and D-Entropy in the Physics of Evolution

The purpose of the paper is to substantiate the possibility of constructing the physics of the evolution of matter based on the fundamental laws of physics. It is shown how this can be done within the framework of an extension of classical mechanics. Its expansion is based on the motion equation of a structured body. The fundamental difference between this equation and Newton’s motion equation is that instead of a model of a body in the form of a material point, it uses a structured body in the form of a system of potentially interacting material points. To obtain this equation, the principle of symmetry dualism, new for classical mechanics, was used. According to this principle, the dynamics of a body are determined not only by the symmetries of space, as in the case of a structureless body, but also by its symmetries. Thanks to this derivation of the equation, it takes into account the fact that the work of external forces, in addition to changing the body’s motion energy, also changes its internal energy. This change occurs due to the body’s motion energy when it moves in a non-uniform field of forces. It is shown why the motion equation of a structured body is irreversible. Its irreversibility made it possible to introduce the concept of D-entropy into extended classical mechanics. It is defined as the value of the relative increase in the body’s internal energy due to the motion energy. The relationship between the values of motion energy and D-entropy in the process of matter evolution is considered. It is shown how this connection is realized during the transition from one hierarchical level of matter to the next level. As a result, it was possible to prove that the evolution of the hierarchical structure of matter is characterized by the relationship between D-entropy and the motion energy of elements at each of its hierarchical levels.