Nonequilibrium Statistical Operator Method Research Articles

Comparison of extended irreversible thermodynamics and nonequilibrium statistical operator method with thermodynamics based on a distribution containing the first-passage time

Comparison of extended irreversible thermodynamics and nonequilibrium statistical operator method with thermodynamics based on a distribution containing the first-passage time

Diffusion in a binary mixture of molecules adsorbed on a multisite two-dimensional lattice

The diffusion in a binary mixture of species coadsorbed on a multisite square lattice is investigated by a theoretical approach (Chumak and Tarasenko, 1980) based on the non-equilibrium statistical operator method proposed by Zubarev (1961). The investigated lattice gas system is rather complex. There is a mixture of two types of particles (atoms, and/or molecules) adsorbed on a multisite lattice which consists of the three types of adsorption sites. This lattice can be subdivided onto three homogeneous square sublattices composed of the sites of the same type. As the binding energies for the molecules of distinct types adsorbed on the nonidentical sublattices are different, there are six average occupancies (coverages) describing the molecule distribution over the sublattices. A system of the balance equations, which controls the exchange of the molecules between the sublattices on the atomistic level is reduced to the diffusion equations describing the evolution of small hydrodynamic fluctuations of these coverages on the macroscopic level. The diffusion equations are written in the Onsager representation, when the driving forces are gradients of the chemical potentials and in the Fickian representation, when the driving forces are the gradients of coverages. The derivation of these equations results in the analytical expressions for the Fickian diffusivities and Onsager phenomenological coefficients. Despite the complex process of derivation, the final results are simple. The kinetic coefficients, which describe the non-equilibrium state of the molecule system, are expressed via the thermodynamic quantities calculated in the equilibrium state of the system: the chemical potentials (or activities), pair correlation functions and the isothermal susceptibilities. These expressions are derived with account of the lateral interactions between the nearest neighbor molecules. The matrix of the Fickian diffusivities has the ordinary classical form. The diffusivity is a non-symmetric 2 × 2 matrix. The Onsager coefficients are represented by a diagonal 2 × 2 matrix, where the cross terms are absent.

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.

Ultrafast dynamics of carriers and phonons of photoinjected double-plasma in aluminium nitride

Aluminum nitride is attracting great interest of the industry and scientific community due to its interesting properties. In this paper is performed a theoretical study on the ultrafast transient transport properties of photoinjected carriers in wurtzite AlN subjected to electric fields up to 80 kV/cm. For this, the Nonequilibrium Statistical Operator Method was used. The evolution towards the steady state of drift velocity of carriers (electrons and holes) and nonequilibrium temperature (carriers and phonons) subpicosecond scale were determined.

Electron Mobility in Bulk n-Doped SiC-Polytypes 3C-SiC, 4H-SiC, and 6H-SiC: A Comparison

This communication presents a comparative study on the charge transport (in transient and steady state) in bulk n-type doped SiC-polytypes: 3C-SiC, 4H-SiC and 6H-SiC. The time evolution of the basic macrovariables: the “electron drift velocity” and the “non-equilibrium temperature” are obtained theoretically by using a Non-Equilibrium Quantum Kinetic Theory, derived from the method of Nonequilibrium Statistical Operator (NSO). The dependence on the intensity and orientation of the applied electric field of this macrovariables and mobility are derived and analyzed. From the results obtained in this paper, the most attractive of these semiconductors for applications requiring greater electronic mobility is the polytype 4H-SiC with the electric field applied perpendicular to the c-axis.

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.

Nonequilibrium information entropy approach to ternary fission of actinides

Ternary fission of actinides probes the state of the nucleus at scission. Light clusters are produced in space and time very close to the scission point. Within the nonequilibrium statistical operator method, a generalized Gibbs distribution is constructed from the information given by the observed yields of isotopes. Using this relevant statistical operator, yields are calculated taking excited states and continuum correlations into account, in accordance with the virial expansion of the equation of state. Clusters with mass number $A \le 10$ are well described using the nonequilibrium generalizations of temperature and chemical potentials. Improving the virial expansion, in-medium effects may become of importance in determining the contribution of weakly bound states and continuum correlations to the intrinsic partition function. Yields of larger clusters, which fail to reach this quasi-equilibrium form of the relevant distribution, are described by nucleation kinetics, and a saddle-to-scission relaxation time of about 7000 fm/c is inferred. Light charged particle emission, described by reaction kinetics and virial expansions, may therefore be regarded as a very important tool to probe the nonequilibrium time evolution of actinide nuclei during fission.

Hot carrier dynamics of photoinjected plasma in indium nitride

A theoretical study using the nonequilibrium statistical operator method is performed to investigate the ultrafast transient transport properties of photoexcited carriers in wurtzite InN subjected to electric fields up to 20 kV/cm. The evolution toward the steady state of the drift velocity of carriers (electrons and holes) and nonequilibrium temperature (carriers and phonons) is determined. The transient regime occurs at the subpicosecond scale with maxima and minima in the hole and electron drift velocities.

Statistical theory of catalytic hydrogen oxidation processes. Basic equations

A statistical description for the processes of catalytic hydrogen oxidation is proposed taking into account the reaction--diffusion processes for magnetoactive ions and atoms adsorbed on the metal surface. The basic non-Markov transfer equations are obtained for the abbreviated description parameters of reaction-diffusion processes for magnetoactive ions and atoms adsorbed on the metal surface in the method of nonequilibrium statistical Zubarev operator. Weakly nonequilibrium reaction-diffusion processes are also considered.

Time Evolution of Open Nonequilibrium Systems and Irreversibility

The foundation of the nonequilibrium statistical mechanics on the basis of dynamics was formulated by Bogoliubov in his seminal works. In this report we use his ideas of reduced description to analyze thoroughly the time evolution of open systems in the context of nonequilibrium statistical operator method. In particular, we consider the notion of entropy which is a central physical concept. The thermodynamic entropy, information entropy, entropy of nonequilibrium states and entropy production were discussed tightly in this context. The corresponding procedure of averaging (smoothing) and the notion of irreversibility were discussed as well.

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.

Anisotropic Carrier Transport in n-Doped 6H-SiC

In this paper, a study is presented on the charge transport in n-type doped semiconductor 6H-SiC (in both transient and steady state) using a nonequilibrium quantum kinetic theory derived from the method of nonequilibrium statistical operator (NSO), which furnishes a clear description of the irreversible phenomena that occur in the evolution of the analyzed system. We obtain theoretically the dependence on the electric field (applied in the orientation perpendicular or parallel to the c-axis) of the basic macrovariables: the electron drift velocity and the nonequilibrium temperature. The peak points in time evolution of this macrovariables are derived and analyzed.

Electron transport in bulk n-doped 3C-SiC by using a non-equilibrium quantum kinetic theory

In this paper we present a study on the charge transport in bulk n-type doped semiconductor 3C-SiC (in both, transient and steady state) using a non-equilibrium quantum kinetic theory derived from the method of nonequilibrium statistical operator (NSO), which furnishes a clear description of the irreversible phenomena that occur in the evolution of the analyzed system. We obtain theoretically the dependence on the applied electric field of the basic macrovariables: the “electron drift velocity” and the “non-equilibrium temperature”. The “peak points” in time evolution of this macrovariables are derived and analyzed.

Microscopic derivation of coarse-grained, energy-conserving generalized Langevin dynamics.

Properly simulating nonequilibrium phenomena such as thermal transport and shock wave propagation in complex condensed matter systems require the conservation of system's internal energy. This precludes the application of the coarse-grained (CG) generalized Langevin equation (GLE) dynamics due to the presence of dissipative interactions. Attempts to address this issue have been pursued both phenomenologically and from entropy-based first principles for dissipative particle dynamics (DPD, a Markovian variant of the CG GLE dynamics) by introducing an energy conserving extension of DPD (DPD-E). We present here a rigorous microscopic derivation of two energy conserving variants of the CG GLE dynamics by extending the CG equations of motion to include the GLE for certain internal energy observables of the microscopic system. We consider two choices of such observables: the total internal energy and a set of internal energies of the CG particles. The derivation is performed using the Mori-Zwanzig projection operator method in the Heisenberg picture for time evolution of thermodynamic expectations and the recently introduced interpretation of the Zwanzig projection operator [S. Izvekov, J. Chem. Phys. 146(12), 124109 (2017)] which allows an exact calculation of the memory and projected terms. We begin with equilibrium conditions and show that the GLE dynamics for the internal energy observables is purely dissipative. Our extension of the GLE dynamics to quasiequilibrium conditions (necessary to observe heat transport) is based on the generalized canonical ensemble approach and transport equation using the nonequilibrium statistical operator (NSO) method. We derive closed microscopic expressions for conductive heat transfer coefficients in the limit of neglecting dissipation in heat transfer and in the lowest order of deviation from equilibrium. After employing the Markov approximation, we compare the equations of motion to the published DPD-E equations. Our equations contain additional energy transfer terms not reported in the previous works. Additionally, we show that, despite neglecting dissipative processes in heat transport, the heat transfer coefficients and random force are related in a way reminiscent of the fluctuation-dissipation relation. The formalism presented here is sufficiently general for the rigorous formulation of the GLE dynamics for arbitrary microscopic phase space observables as well as sampling different microscopic ensembles in CG simulations.

Application of the Non-Equilibrium Statistical Operator Method to the Dynamical Conductivity of Metallic and Classical Plasmas

The fruitfulness of the method of a non-equilibrium statistical operator (NSO) and generalized linear response theory is demonstrated calculating the permittivity, dynamical conductivity, absorption coefficient, and dynamical collision frequency of plasmas in the degenerate, metallic state as well as classical plasmas. A wide range of plasma parameters is considered, and a wide range of frequencies of laser radiation acting on such plasmas is treated. New analytical expressions for the plasma response are obtained by this method, and several limiting cases are discussed.

Unification of Thermo Field Kinetic and Hydrodynamics Approaches in the Theory of Dense Quantum–Field Systems

A formulation of nonequilibrium thermo-field dynamics has been performed using the nonequilibrium statistical operator method by D.N. Zubarev. Generalized transfer equations for a consistent description of the kinetics and hydrodynamics of the dense quantum field system with strongly-bound states are derived.

Generalized transport equation with nonlocality of space–time. Zubarev’s NSO method

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 Renyi statistics. New non-Markovian diffusion equations for particles in spatially heterogeneous environment with fractal structure and a generalized Cattaneo-type diffusion equation with taking into account nonlocality of space–time are obtained. Different models of frequency-dependent memory functions, which lead to known diffusion equations with nonlocality of space–time and their generalizations are studied.

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.

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.

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