arXiv subjects
Publications and source records attributed to V. M. Somsikov.
The mechanics of the structured particles develops. The substantiation of applicability of such mechanics for the description of processes of evolution in open nonequilibrium systems is offered. The consequences following from the equations of dynamics of structured particles are analyzed.
The mechanics of structured particles (SP) consisting from potentially interacting material points are discussed. For this purpose the derivation of the SP equation motion in the field of external forces is submitted. The differences between the properties of the dynamics of material point and properties of the dynamics of SP are analyzed. The explanation of how mechanics of the $SP$ leads to the account of dissipative forces is submitted. The derivation of Lagrange, Hamilton and Liouville equations for $SP$ Is shown. The question of why the motions of the SP are determined by the two types of symmetry: internal symmetry of the system and symmetry of space and how it leads to two types of energy and forces accordingly are discussed. It is shown how the concept of entropy arises in classical mechanics. The question how the mechanics of the SP leads to thermodynamics, statistical physics and kinetics is explained.
The principles of creation of the mechanics of structured particles in the frame of the Newton's laws are considered. The explanation how this mechanics leads to the account of dissipative forces is offered. Why the motions of the system determine by two type of symmetry: symmetry of the system and symmetry of space and how it leads to two types of energy and forces accordingly are discussed. How the mechanics of the structured particles leads to thermodynamics, statistical physics and kinetics are explained.
Dynamics of the structured particles consisting of potentially interacting material points is considered in the framework of classical mechanics. Equations of interaction and motion of structured particles have been derived. The expression for friction force has been obtained. It has been shown that irreversibility of dynamics of structured particles is caused by increase of their internal energy due to the energy of motion. It has been shown also that the dynamics of the structured particles is determined by two types of symmetry: the symmetry of the space and the internal symmetry of the structured particles. Possibility of theoretical substantiation of the laws of thermodynamics has been considered.
Dynamics of systems of structured particles consisting of potentially interacting material points is considered in the framework of classical mechanics. Equations of interaction and motion of structured particles have been derived. The expression for friction force has been obtained. It has been shown that irreversibility of dynamics of structured particles is caused by increase of their internal energy due to the energy of motion. Possibility of theoretical substantiation of the laws of thermodynamics has been considered.
The reasons which restrict opportunities of classical mechanics at the description of nonequilibrium systems are discussed. The way of overcoming of the key restrictions is offered. This way is based on an opportunity of representation of nonequilibrium system as a set of equilibrium subsystems. The equation of motion and the general Lagrange, Hamilton and Liouville equations for subsystems have been obtained. The way of a substantiation of thermodynamics is offered.
Within the frames of the analytical mechanics the method of the description of dynamics of nonequilibrium systems of potentially interacting elements is develops. The method is based on an opportunity of representation of nonequilibrium system by set of interacting equilibrium subsystems. The equation of motion of interacting subsystems is found. Based on it the Lagrange, Hamilton and Liouville equations for subsystems are obtained. The expression of an entropy production is found. The way of a substantiation of thermodynamics in the frames of classical mechanic is offered.
The expansion of a classical Hamilton formalism consisting in adaptation of it to describe the nonequilibrium systems is offered. Expansion is obtained by construction of formalism on the basis of the dynamics equation of the equilibrium subsystems by which the nonequilibrium system is represented. It has allowed removing restrictions on dynamics of the subsystems, which dictated by the requirement of monogenic and potentiality of the forces between subsystems. Modified Lagrange, Hamilton and Liouville equations are obtained. Some features of dynamics of nonequilibrium systems are considered. Connection between the equation of interaction of subsystems and a thermodynamic principle of energy is analyzed.
An explanation of the mechanism of irreversible dynamics was offered. The explanation was obtained within the framework of laws of classical mechanics by the expansion of Hamilton formalism. Such expansion consisted in adaptation of it to describe of the non-potential interaction of a systems. The procedure of splitting of a system into equilibrium subsystems, presentation of subsystem's energy as the sum of energy of their relative motion and their internal energy was the basis of the approach which was used for the analysis of nonequilibrium systems. As a results the generalized Liouville equation and equation of subsystems interaction was obtained. Based on these equations, the irreversible transformation of energy of the relative motion of subsystems into their internal energy was proved. The formula which expresses the entropy via the work of subsystems' interaction forces was submitted. The link between classical mechanics and thermodynamics was discussed.
The process of equilibration of a colliding hard-disks system is studied in the framework of classical mechanic. The method consists of dividing the nonequilibrium system into the interacting subsystems; the evolution one of these subsystems is analyzed employing generalized Lagrange and Liouville equations. The subsystem-subsystem interaction force is considered as an evolution parameter. The mechanism by which its system equilibrates is described.
The mechanism of irreversible dynamics in the mixing systems is constructed in the frames of the classical mechanics laws. The offered mechanism can be found only within the framework of the generalized Hamilton's formalism. The generalized formalism is created by expansion of the canonical Hamilton's formalism to the open systems. A formula, which expresses the entropy through the work of subsystems interaction forces was obtained. The essential link between thermodynamics and classical mechanics was established.
The mechanism of irreversible dynamics in the systems with mixing is analyzed. The procedure of splitting of system on equilibrium subsystems and studying of dynamics of one of them under condition of its interaction with other subsystems in the basis of the approach to the analysis of dynamics of nonequilibrium systems is used. The problem of "coarse-grain" of the phase space in this method is eliminated. The formula, which expresses the entropy through the work of forces between systems, is submitted. The essential link between thermodynamics and classical mechanics was found.
The approach to a substantiation of thermodynamics is offered. A conservative system of interacting elements, which is not in equilibrium, is used as a model. This system is then split into small subsystems that are accepted as being in equilibrium. Based on the D'Alambert equation for a subsystem the generalized Liouville equation is obtained. A necessary condition for irreversibility is determined. This condition is dependence the forces of interaction of subsystems on relative velocities. The equation of motion of subsystems of potentially interacting elements is obtained. The non-potentiality of the forces of interaction of the subsystems consisting of potentially interacting elements is proved. The mechanism of occurrence of irreversible dynamics is offered. The formula that expresses the entropy through the forces of interaction of subsystems is obtained. The theoretical link between classical mechanics and thermodynamics is analyzed.
The irreversibility of the dynamics of the conservative systems on example of hard disks and potentially of interacting elements is investigated in terms of laws of classical mechanics. The equation of the motion of interacting systems and the formula, which expresses the entropy through the generalized forces, are obtained. The explanation of irreversibility mechanism is submitted. The intrinsic link between thermodynamics and classical mechanics was analyzed.
The approach to the analysis of the dynamic of non-equilibrium open systems within the framework of the laws of classical mechanics on the example a hard-disks is offered. This approach was based on Hamilton and Liouville generalized equations which was deduced for the subsystems of the nonequilibrium system. With the help of generalized Liouville equation it was obtained that two types of dynamics are possible: reversible and irreversible. The connection between the dynamical parameter -generalized field of forces, and entropy is established. The estimation of characteristic time of establishment of equilibrium in the thermodynamic limit is realized. It is shown how from the condition of irreversibility of a hard-disk system, the condition of irreversibility for the rarefied system of potentially interacting particles follows. The explanation of the mechanism of irreversibility is submitted.