Zubarev Nonequilibrium Statistical Operator Research Articles

Cross effects in spin hydrodynamics: Entropy analysis and statistical operator

We revisit the construction of first-order spin hydrodynamics and find that the constitution relations receive the corrections from the cross effects resulting from spin-orbit coupling. Starting from a routine entropy analysis, we show how to identify cross effects and new cross transport coefficients from the second law of thermodynamics. Interestingly, the conventional transport coefficient heat conductivity $\kappa$ is bounded from below by the product of cross transport coefficients, which means the threshold of heat conduction is changed. With recourse to Zubarev's non-equilibrium statistical operator, we reproduce the construction of first-order spin hydrodynamics and identification of cross effects in a more rigorous way. By seeking the dispersion relations of normal modes, we find that these cross effects suppress the attenuation of sound modes and heat mode appearing in conventional hydrodynamics and also have impacts on the damping of non-hydrodynamic spin modes.

Generalized diffusion equation with nonlocality of space-time: Analytical and numerical analysis

We present a general approach for obtaining the generalized transport equations for weakly nonequilibrium processes with fractional derivatives by using the Liouville equation with fractional derivatives for a system of classical particles and the Zubarev nonequilibrium statistical operator method. A generalized diffusion equation for a system of classical particles in fractional derivatives is obtained for weakly nonequilibrium processes. Based on the non-Markov diffusion equation, taking into account the spatial nonlocality and modeling the generalized coefficient of particle diffusion Dαα′(r,r′;t,t′)=W(t,t′)D̄αα′(r,r′) using fractional calculus, the generalized Cattaneo–Maxwell-type diffusion equation in fractional time and space derivatives is obtained. In the case of a constant diffusion coefficient, analytical and numerical studies of the frequency spectrum for the Cattaneo–Maxwell diffusion equation in fractional time and space derivatives are performed. Numerical calculations of the phase and group velocities with a change in values of characteristic relaxation time, diffusion coefficient, and indices of temporal ξ and spatial α nonlocality are carried out.

Kubo formulae for first-order spin hydrodynamics

We derive Kubo formulae for first-order spin hydrodynamics based on non-equilibrium statistical operators method. In first-order spin hydrodynamics, there are two new transport coefficients besides the ordinary ones appearing in first-order viscous hydrodynamics. They emerge due to the incorporation of the spin degree of freedom into fluids and the spin-orbital coupling. Zubarev's non-equilibrium statistical operator method can be well applied to investigate these quantum effects in fluids. The Kubo formulae, based on the method of non-equilibrium statistical operators, are related to equilibrium (imaginary-time) infrared Green's functions, and all the transport coefficients can be determined when the microscopic theory is specified.

Generalized diffusion equation with nonlocality of space-time. Memory function modelling

We presented a general approach for obtaining the generalized transport equations with fractional derivatives by using the Liouville equation with fractional derivatives for a system of classical particles and Zubarev's nonequilibrium statistical operator (NSO) method within Gibbs statistics. The new non-Markovian diffusion equations of ions in spatially heterogeneous environment with fractal structure and generalized Cattaneo-Maxwell diffusion equation with taking into account the space-time nonlocality are obtained. Dispersion relations are found for the Cattaneo-Maxwell diffusion equation with taking into account the space-time nonlocality in fractional derivatives. The frequency spectrum, phase and group velocities are calculated. It is shown that it has a wave behaviour with discontinuities, which are also manifested in the behaviour of the phase velocity.

Generalized Electrodiffusion Equation with Fractality of Space-Time: Experiment and Theory.

Physical and technological principles of formation of clathrate structures for supramolecular electronics are given in this paper. It has been established that supramolecular nature of the "host-guest" conjunction, in general, and hierarchical architecture of the corresponding clathrates, in particular, provide realization of such an extraordinary effect as an optically or a magnetically controlled phenomenon of colossal "negative capacity" with a predicted frequency interval of manifestation, magnitude, and multiplicity. For the first time, the experimental confirmation of the behavior of the electretized fractal clathrate GaSe⟨β-CD⟨FeSO4⟩⟩ as a dissipative element, which accumulates inductive energy, is demonstrated. A general approach for obtaining the generalized transport equations with fractional derivatives by using the Liouville equation with fractional derivatives for a system of classical particles and the Zubarev nonequilibrium statistical operator method within Renyi statistics is presented. New non-Markovian electrodiffusion equations for ions in a spatially heterogeneous medium with the fractal structure and a generalized Cattaneo-type diffusion equation taking into account the fractality of space-time are obtained. The model of subdiffusion impedance based on the Cattaneo equation with fractional derivatives is applied to multilayer nanostructures. Nyquist diagrams for different valuses of the parameter τ (delay time of a flow relative to a concentration gradient) and the subdiffusion coefficient Dα are calculated.

Statistical irreversible thermodynamics in the framework of Zubarev's nonequilibrium statistical operator method

Statistical irreversible thermodynamics in the framework of Zubarev's nonequilibrium statistical operator method

Nonequilibrium Statistical Operator Method and Generalized Kinetic Equations

We consider some principal problems of nonequilibrium statistical thermodynamics in the framework of the Zubarev nonequilibrium statistical operator approach. We present a brief comparative analysis of some approaches to describing irreversible processes based on the concept of nonequilibrium Gibbs ensembles and their applicability to describing nonequilibrium processes. We discuss the derivation of generalized kinetic equations for a system in a heat bath. We obtain and analyze a damped Schrodinger-type equation for a dynamical system in a heat bath. We study the dynamical behavior of a particle in a medium taking the dissipation effects into account. We consider the scattering problem for neutrons in a nonequilibrium medium and derive a generalized Van Hove formula. We show that the nonequilibrium statistical operator method is an effective, convenient tool for describing irreversible processes in condensed matter.

BBGKY chain of kinetic equations, non-equilibrium statistical operator method and collective variable method in the statistical theory of non-equilibrium liquids

A chain of kinetic equations for non-equilibrium one-particle, two-particle and $ s $-particle distribution functions of particles which take into account nonlinear hydrodynamic fluctuations is proposed. The method of Zubarev non-equilibrium statistical operator with projection is used. Nonlinear hydrodynamic fluctuations are described with non-equilibrium distribution function of collective variables that satisfies generalized Fokker-Planck equation. On the basis of the method of collective variables, a scheme of calculation of non-equilibrium structural distribution function of collective variables and their hydrodynamic speeds (above Gaussian approximation) contained in the generalized Fokker-Planck equation for the non-equilibrium distribution function of collective variables is proposed. Contributions of short- and long-range interactions between particles are separated, so that the short-range interactions (for example, the model of hard spheres) are described in the coordinate space, while the long-range interactions --- in the space of collective variables. Short-ranged component is regarded as basic, and corresponds to the BBGKY chain of equations for the model of hard spheres.

Generalized diffusion equation with fractional derivatives within Renyi statistics

By using the Zubarev nonequilibrium statistical operator method, and the Liouville equation with fractional derivatives, a generalized diffusion equation with fractional derivatives is obtained within the Renyi statistics. Averaging in generalized diffusion coefficient is performed with a power distribution with the Renyi parameter q.

Generalized kinetic equations for dense gases and liquids in the Zubarev nonequilibrium statistical operator method and Renyi statistics

To describe kinetic processes in gases and liquids far from equilibrium, we obtain the nonequilibrium statistical operator (NSO) and the generalized kinetic equations for the nonequilibrium one- and two-particle distribution functions based on the Zubarev NSO method and the maximum entropy principle for the Renyi entropy. We consider a q-generalization of the Liouville equation and obtain its general solution using the NSO method.

Zubarev nonequilibrium statistical operator method in Renyi statistics. Reaction-diffusion processes

The Zubarev nonequilibrium statistical operator (NSO) method in Renyi statistics is discussed. The solution of $q$-parametrized Liouville equation within the NSO method is obtained. A statistical approach for a consistent description of reaction-diffusion processes in "gas-adsorbate-metal" system is proposed using the NSO method in Renyi statistics.

Consistent description of kinetics and hydrodynamics of dusty plasma

A consistent statistical description of kinetics and hydrodynamics of dusty plasma is proposed based on the Zubarev nonequilibrium statistical operator method. For the case of partial dynamics the nonequilibrium statistical operator and the generalized transport equations for a consistent description of kinetics of dust particles and hydrodynamics of electrons, ions and neutral atoms are obtained. In the approximation of weakly nonequilibrium process a spectrum of collective excitations of dusty plasma is investigated in the hydrodynamic limit.

Dielectric Properties of Monoclinic RbD2PO4. The Influence of Hydrostatic Pressure

We proposed a modified proton ordering model for the quasi-one-dimensional monoclinic RbD2PO4, that takes into account linear over strains ϵi and ϵ5 contributions to the proton subsystem energy. Within the framework of the model, using the two-particle cluster approximation we calculate the static dielectric permittivity of the crystal. The dynamic dielectric permittivity of the crystal is calculated within the D.N. Zubarev nonequilibrium statistical operator method. The available experimental data for static and dynamic permittivities, are described. The effect of hydrostatic pressure on the physical characteristics of the crystal is explored.

Statistical description of hydrodynamic processes in ionic melts while taking into account polarization effects

A statistical description of hydrodynamic processes for molten salts is proposed taking into account polarization effects caused by the deformation of external ionic shells. This description is conducted by means of the Zubarev nonequilibrium statistical operator method, appropriate for researches of both strong and weak nonequilibrium processes. The nonequilibrium statistical operator and the generalized hydrodynamic equations that take into account the polarization processes are acquired for the ion-polarization model of ionic molten salts when the nonequilibrium averaged values of densities of ions number, their momentum, dipole momentum, and total energy are chosen for the reduced description parameters. A spectrum of collective excitations is investigated within the viscoelastic approximation for the ion-polarization model of ionic melts.

Nonequilibrium statistical operator method in Renyi statistics

The generalization of the Zubarev nonequilibrium statistical operator (NSO) method for the case of Renyi statistics is proposed when the relevant statistical operator (or distribution function) is obtained based on the maximum entropy principle for the Renyi entropy. The nonequilibrium statistical operator and corresponding generalized transport equations for the reduced-description parameters are obtained. A consistent description of the kinetic and hydrodynamic processes in a system of interacting particles is considered as an example.

Relaxation to the state of molecular hydrodynamics in the generalized hydrodynamics of liquids

The problem of relaxation of a nonequilibrium state to the state of molecular hydrodynamics is considered for a classical system of interacting particles using the Zubarev nonequilibrium statistical operator method. The wave-vector and frequency dependencies of the dynamical structure factor and momentum-momentum transverse correlation function are investigated on the basis of the appropriate generalized transport equations. Comparison with the results of molecular hydrodynamics and molecular-dynamics simulations is given and the characteristic time intervals of the studied relaxation processes are determined.

Nonequilibrium statistical operator in the generalized hydrodynamics of fluids

The investigations of the classical interacting particles systems far from equilibrium using the Zubarev nonequilibrium statistical operator method are presented. The problem of the relaxation of a nonequilibrium state of a system to the state of molecular hydrodynamics is considered. The nonequilibrium statistical operator and the appropriate transport equations which describe such a relaxation process are obtained. Explicit expressions for dynamic structure factor and momentum-momentum time correlation function are obtained by solving the set of equations for time correlation functions and some numerical results are presented.

Nonequilibrium statistical operator in the generalized molecular hydrodynamics of fluids

We discuss the important role of the Zubarev nonequilibrium statistical operator method in the generalized molecular hydrodynamics of fluids. Using this method allows developing a consistent approach of generalized collective excitations for simple, ion, polar, magnetic, and some other fluids. We construct a nonequilibrium statistical operator and derive the corresponding transport equations for a system that relaxes and passes into the state of molecular hydrodynamics.

Description of isolated macroscopic systems inside quantum mechanics

For an isolated macrosystem classical state parameters ζ( t) are introduced inside a quantum mechanical treatment. By a suitable mathematical representation of the actual preparation procedure in the time interval [ T, t 0] a statistical operator is constructed as a solution of the Liouville—von Neumann equation, exhibiting at time t the state parameters ζ( t′), t 0 ≤ t′ ≤ t, and preparation parameters related to times T ≤ t′ ≤ t 0. Relation with Zubarev's nonequilibrium statistical operator is discussed. A mechanism for memory loss is investigated and time evolution by a semigroup is obtained for a restricted set of relevant observables, slowly varying on a suitable time scale.

<![CDATA[<b>Flux Operators of Microdynamical Quantities in a Nonequilibrium Statistical Ensemble Formalism</b>]]>

It is shown how the closure condition for the set of kinetic equations in Zubarev's Nonequilibrium Statistical Operator Method introduces a series of fluxes of a reference set of densities. These fluxes are the average values, over a Gibbs-like nonequilibrium generalized grand-canonical ensemble, of Hermitian operators for fluxes defined at the microscopic-mechanical level. The equations of evolution for these fluxes (or equivalently for their conjugated Lagrange multipliers) are described.