INTERNAL TIME OF A MECHANICAL SYSTEM

Abstract

One of the most urgent unsolved problems of modern science is the extension of the second law of thermodynamics to conservative mechanical systems that are in a state far from thermodynamic equilibrium. How does the collective motion of the material points of the system, each of which is described by time-reversible equations, become irreversible? Thus, the increase in entropy of an ideal gas in a state close to equilibrium indicates the irreversible nature of the evolution of a conservative mechanical system, which is definitely an ideal gas. That is, entropy acts as internal time and sets the direction to the future or the "arrow of time". The paper deals with obtaining a characteristic of a conservative mechanical system that would have the properties of entropy. The goal is to extend the second law of thermodynamics to conservative mechanical systems that are in a state far from equilibrium. Analytical methods were used to analyze the differential equations of motion of a phase liquid particle as an image of a mechanical system in a multidimensional space. The evolution of the distribution of the probability of a particle of a phase fluid staying on a hypersurface of equal energy is considered. For a conservative mechanical system, a value is introduced whose properties allow us to apply the term "internal time" to it. Its growth determines the difference between future events and past events, which is an inherent property of subjective time. When approaching the state of equilibrium, internal time slows down, and physical time, accordingly, accelerates relative to internal time. Internal time is as universal as physical time, in the sense that it is determined for each system by a universal formula. The proposed approach made it possible to solve the fundamental problem of replacing the averaging of the probability density in the phase space by averaging in time along the trajectory of the point in the phase space. We used the fact that the equation of motion of a conservative system can be obtained as the equation of motion of a particle of a phase liquid, using the law of conservation of matter. The equations of motion of a particle were transferred to the motion of a point. In contrast, when using the traditional approach, the equation of motion of a point in phase space was taken as the basic law of nature. An understanding of internal time allows us understand the emergence of dissipative structures in the future.