Nonequilibrium Statistical Operator 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

Hydrodynamic fluctuations, diffusion and correlation functions in systems of particles adsorbed on solid surfaces

We present the detailed derivation of the equations describing the evolution of the hydrodynamic fluctuations of the coverage of particles adsorbed on homogeneous lattices. Using the method of the non-equilibrium statistical operator, we reduce the balance equation governing the behavior of the individual particles to the diffusion equation. On a macroscopic level, this equation describes the approach to equilibrium of the hydrodynamic coverage fluctuations. We obtain the analytical expressions for the Fickian diffusivity and Onsager phenomenological coefficient. These expressions are derived with account of the lateral interaction between the particles. They are simple functions of the thermodynamic quantities — derivatives of the thermodynamic potential over its arguments. The transport coefficients accurately describe the development of fluctuations in the entire coverage region and in the wide range of lateral interactions. We presented an elementary introduction to the theory of fluctuations in the lattice gas systems. For calculations of the correlation function and spectral density of fluctuations, we use the Langevin approach and the method of moments. The exact coincidence of the analytical expressions for the diffusion coefficients obtained by the two independent calculations is the direct proof of the accuracy of the approach developed in Chumak and Tarasenko (1980).

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.

Thermodynamic-induced geometry of self-gravitating systems

A new approach based on the nonequilibrium statistical operator is presented that makes it possible to take into account the inhomogeneous particle distribution and provides obtaining all thermodynamic relations of self-gravitating systems. The equations corresponding to the extremum of the partition function completely reproduce the well-known equations of the general theory of relativity. Guided by the principle of Mach's "economing of thinking" quantitatively and qualitatively, is shown that the classical statistical description and the associated thermodynamic relations reproduce Einstein's gravitational equation. The article answers the question of how is it possible to substantiate the general relativistic equations in terms of the statistical methods for the description of the behavior of the system in the classical case.

New Developments in Relativistic Magnetohydrodynamics

Relativistic magnetohydrodynamics (RMHD) provides an extremely useful description of the low-energy long-wavelength phenomena in a variety of physical systems from quark–gluon plasma in heavy-ion collisions to matters in supernova, compact stars, and early universe. We review the recent theoretical progresses of RMHD, such as a formulation of RMHD from the perspective of magnetic flux conservation using the entropy–current analysis, the nonequilibrium statistical operator approach applied to quantum electrodynamics, and the relativistic kinetic theory. We discuss how the transport coefficients in RMHD are computed in kinetic theory and perturbative quantum field theories. We also explore the collective modes and instabilities in RMHD with a special emphasis on the role of chirality in a parity-odd plasma. We also give some future prospects of RMHD, including the interaction with spin hydrodynamics and the new kinetic framework with magnetic flux conservation.

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.

Revisiting relativistic magnetohydrodynamics from quantum electrodynamics

We provide a statistical mechanical derivation of relativistic magnetohydrodynamics on the basis of (3 + 1)-dimensional quantum electrodynamics; the system endowed with a magnetic one-form symmetry. The conservation laws and constitutive relations are presented in a manifestly covariant way with respect to the general coordinate transformation. The method of the local Gibbs ensemble (or nonequilibrium statistical operator) combined with the path-integral formula for a thermodynamic functional enables us to obtain exact forms of constitutive relations. Applying the derivative expansion to exact formulas, we derive the first-order constitutive relations for nonlinear relativistic magnetohydrodynamics. Our results for the QED plasma preserving parity and charge-conjugation symmetries are equipped with two electrical resistivities and five (three bulk and two shear) viscosities. We also show that those transport coefficients satisfy the Onsager’s reciprocal relation and a set of inequalities, indicating semi-positivity of the entropy production rate consistent with the local second law of thermodynamics.

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.

Statistical Description of Non-Equilibrium Many-Particle Systems

In most cases, the systems of interacting particles are non-equilibrium. In this review, a new approach based on the application of a non-equilibrium statistical operator is presented, which allows the inhomogeneous distributions of the particles and the temperature to be taken into account. The method uses the saddle-point procedure to find dominant contributions to the partition function of the system and enables all of its thermodynamic parameters to be determined. Probable peculiarities in the behavior of the systems with interaction – such as gravitational systems, systems with Coulombic repulsion, and so forth – under various thermodynamic conditions are predicted. A new approach is proposed to describe non-equilibrium systems in the energy space, which is an extension of the Gibbs approach to macroscopic systems under non-equilibrium conditions. It allows the stationary states and the dynamics of non-equilibrium systems to be described.

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.

Nonequilibrium Pion Distribution within the Zubarev Approach

We discuss how the non-equilibrium process of pion production within the Zubarev approach of the non-equilibrium statistical operator leads to a theoretical foundation for the appearance of a non-equilibrium pion chemical potential for the pion distribution function for which there is experimental evidence in experiments at the CERN LHC.

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.

Microscopic theory of the influence of dipole superparamagnetics (type <beta-CD<FeSO_4>>) on current flow in semiconductor layered structures (type GaSe, InSe)

A statistical approach to description of the charge carrier transfer processes in hybrid nanostructures taking into account electromagnetic fields is proposed using the method of the nonequilibrium statistical operator Zubarev. Generalized transfer equations are obtained, which describe non-Markov processes of charge transfer in the system taking into account magnetic and polarization processes under the influence of external and induced internal electromagnetic fields. Weakly nonequilibrium charge transfer processes in nanostructures are considered, and a nonequilibrium statistical operator is obtained, by means of which the magneto-diffusion transfer equations for electrons in layered nanostructures are obtained. A generalized Cattaneo-type diffusion equation in time fractional derivatives is obtained for electrons with a characteristic relaxation time and a generalized model is proposed that takes into account the complexity of relaxation electro-magnetic diffusion processes for electrons in layered nanostructures.

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.