Exact equation for classical many-particle systems in closed form: from mechanics to statistical thermodynamics

The exact equations of motion for microscopic density of classical particles number with account of inter-particle interactions and external field in closed form are derived. An integral equation for equilibrium distributions of the particles is deduced. No statistical or probabilistic hypotheses and assumption in these deductions have been used. Some well known results of equilibrium statistical mechanics are deduced from the obtained equations as simple limiting cases. The wave equation for almost homogeneous systems with inter-particle interactions are obtained. Connection between inter-particle potential and dispersion law of sound is established. Keywords: Many-body systems dynamics; inter-atomic potentials; phase equilibrium PACS 05.20.-y; 05.10.-a; 05.70.LnComment: 7 page

Irreversibility in two-body system. Toy model

It is shown that the irreversible behavior of classical systems of interacting particles is a common property for both few-body and many-body systems. It is due to the delay in the interactions between the particles. PACS: 45.50.Jf Few- and many-body systems; 82.40.Bj Oscillations, chaos, and bifurcations; 05.70.-a Thermodynamics. Keywords: irreversibility, interactions retardation.Comment: 7 pages, 1 figur

Exact closed probability-free kinetic equation for system of classical particles with retarded interactions: towards microscopic foundation of kinetics

The exact closed equation of motion for microscopic distribution function of classical many-body system with account of interactions retardation between particles is derived. It is shown that interactions retardation leads to irreversible behaviour of many-body systems. PACS: 05.20.Dd ; 05.60.-k; 45.20.-dComment: 5 pages, 21 ref

On physical principles and mathematical mechanisms of the phenomenon of irreversibility

It is shown that the phenomenon of irreversibility in many-body and few-body systems can be explained and described within the framework of the concept of direct (not instantaneous) interaction of particles without using probabilistic hypotheses. The exact solution of the model of a two-particle classical oscillator with retarded interaction between particles is presented. It is established that the interactions retardation leads to appearance of an infinite spectrum of both stationary and non-stationary oscillations, and to non-invariance of the solution with respect to time reversal as well.Comment: 12 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1712.0005

Relativistic kinetic theory of classical systems of charged particles: towards the microscopic foundation of thermodynamics and kinetics

In the complete system of equations of evolution of the classical system of charges and the electromagnetic field generated by them, the field variables are excluded. An exact closed relativistic non-Hamiltonian system of nonlocal kinetic equations, that describes the evolution of a system of charges in terms of their microscopic distribution functions, is obtained . The solutions of this system of equations are non-invariant with respect to time reversal, and also have the property of hereditarity.Comment: 19 pages, 50 reference

A fast algorithm of coexisting phases compositions calculation in binary systems

A simple fast algorithm of the conodes calculation in binary systems is proposed. The method is based on exact solution of the problem on common tangent to pair of approximating parabolas. Sequence of approximating parabolas pairs having second order tangency points on separated concave parts of free energy isotherm is generated. The sequences of the tangency points pairs conodes with approximating parabolas converge to equilibrium compositions of phases in binary systems. PACS: 64.75.-g; 64.10.+h; 05.70.Ce; 82.60.-s Key words: Phase equilibria; Free energy; Binary systems; Conode; Phase diagrams.Comment: 10 pages, 4 figure

Low- and high-temperature anomalies in the physical properties of solid methane

Near 20.48K and in the temperature range 60--70K, anomalous behavior of thermodynamic, spectral, plastic, elastic and other properties of solid methane is observed. The anomalies in the vicinity of 20.48K are due to the phase $\alpha-\beta$ transition. Anomalies in a relatively wide range of 60--70K are shown to be related to the essentially quantum nature of the collective rotation of methane molecules. The provided analysis of the high-temperature anomalies encompasses a more extensive set of phenomena in comparison with the low-temperature ones. Key words: solid methane, anomalies of physical properties, phase transition, rotational temperature, quantum-classical transition.Comment: 12 pages, 16 figures, 18 reference

Generalized Lattice Model of Multi-Component Systems with Internal Degrees of Freedom. II. Quasiequilibrium States

The paper contains an application of the generalized lattice model to multicomponent systems with internal degrees of freedom. The short-range inter-atomic repulsions and smooth long-range parts of the inter-atomic potentials are considered separately by means of packing condition and in effective field approximation, respectively. The dependence of the inter-atomic potentials on the internal degrees of freedoms (such as atomic electric and/or magnetic momentum) taken into account. The Helmholtz free energy functional in the generalized lattice model is reduced to the Ginzburg-Landau-Cahn-Hilliard-like form. The connection between the inter-atomic potentials characteristics and the parameters of the GLCH-like functional is obtained. Equations for both equilibrium and quasi-equilibrium states in condensed systems are derived. It is shown that equilibrium distribution of the fast internal degrees of freedom by frozen space distribution of the components obeys to the Schroedinger-like equation.Comment: 12 page

Modeling of hysteresis phenomena in crystalline ferroelectrics: hysteresis loops shape control by means of electric field parameters

Description of domains switching processes in crystalline ferroelectrics by means of relaxation type equations with account of variable external electric field is proposed. Exact solution of these equations in closed analytical form at arbitrary dependence of electric field on time is obtained. A connection between frequency of sinusoidal external field and hysteresis loops shapes is analysed by numerical way. The calculation results are in qualitative accordance with experimental data. PACS: 77.80.Fm, 77.80.Dj, 77.80.-e Keywords: ferroelectrics, switching process, hysteresis, polarizationComment: 10 pages, 2 figure

Low-frequency internal friction (LFIF) as express-method for identification of cryocrystals in pores of the solids

We show that studying of low-frequency internal friction (LFIF) of solid samples at low temperatures allows determining the presence of various gases absorbed, for some reasons, in pores and caverns of the solids. The gases come over to a solid state (cryocrystals) and exist in the pores under corresponding thermodynamic conditions giving an additional contribution to the LFIF spectra. The spectra reflect the special points of the gases (temperatures of melting or phase transitions). This information gives a real opportunity for identification of gas in the matrix, i.e. the studied solids. This may be of great importance for investigations of cosmic or geological samples, for instance, asteroids, meteorites, rock formations, etc. The LFIF method allows identification of gas media surrounding the studied sample.Comment: 14 pages, 8 figures, 39 ref