Radiation and the violation of bilinearity in the thermodynamics of irreversible processes

Even though irreversible thermodynamics is meant to be a universal theory for nonequilibrium processes, that theory has not taken nonequilibrium radiation processes, which can normally be ignored, into account; thus it is primarily a theory for matter. When the simple bilinear entropy production rate of irreversible thermodynamics is modified, to account for the entropy production due to radiation while preserving local equilibrium for matter, the simple bilinear form of that rate, on which the current theory depends, is lost. Despite substantial compromises, generalized definitions for forces and fluxes cannot restore that simple homogeneous bilinear form, nor do they succeed in generating even generalized bilinearity in the entropy production rates for some problems concerning radiation. The possibility of a broader nonequilibrium theory is suggested by radiation problems, characterized by an example due to Planck, where those generalizations fail and the entropy production rate is a minimum in the steady state.     

Star formation regions as galactic dissipative structures

The theory of dissipative structures, applied to star formation systems, provides a conceptual framework for the study of the behaviour and evolution of these systems. As shown by an analysis of a model star formation process system, prolonged stationary star formation in localized areas and repetitive bursting star formation events can be understood as different behavioural modes of galactic dissipative structures. Young stellar associations with theirHII regions and molecular clouds are manifestations of the ordered distribution of matter participating in the star formation processes. A self-organization with the appearance of ordered structures is, in general, to be expected in nonequilibrium systems in which nonlinear processes occur. However, lacking a thermodynamic theory that can be applied to self-gravitating systems, the behaviour of star-forming regions can only be studied by model calculations simulating the process system within the region.     

Some recent developments in the theoretical dynamics of magnetic fields

This article describes recent developments in the theoretical investigation of magnetostatic equilibrium in the presence of gravity, nonequilibrium in hydromagnetics, and classical problems in hydromagnetic stability. The construction of magnetostatic equilibria has progressed beyond geometrically idealized systems, such as the axisymmetric system, to fully three-dimensional systems capable of modelling realistic solar structures. Nonequilibrium in a magnetic field with an arbitrary interweaving of lines of force due to random footpoint motion is a novel and subtle property with important implications for the solar atmosphere. Work begun by Parker and subsequent developments are described. To the extent quasi-static solar structures are approximated by stable equilibrium, ideal hydromagnetic stability theory provides a first insight into how stability is achieved in the solar environment. A qualitative physical picture based on recent stability analyses is given. The article places emphasis on understanding basic principles and issues rather than detailed results which can be found in the published literature.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Radiation Properties of High-Energy Astrophysical Plasmas

We discuss radiation properties of plasmas in high-energy astrophysics with a keyword nonequilibrium: non-LTE level populations, nonequilibrium ionization, and non-Maxwellian distribution function, beginning with radiative transfer. We focus particularly on supernova remnants interacting with the circumstellar/interstellar matter, and also mention line emission processes in accretion gas onto a neutron star or black hole, and in the X-ray afterglow of γ-ray bursts.     

Emission and absorption of cyclotron radiation in non-equilibrium plasma

From the kinetic Klimontovich theory we derive the equation of radiative transfer for the case of homogeneous and stationary nonequilibrium plasma in a magnetic fiel. For the sake of simplicity we shall consider only the propagation of cyclotron-radiation in the direction of the magnetic field. Explicit expressions for the coefficients of absorption and spontaneous emission, valid also at the cyclotron frequency, will be obtained. In the final results the plasma is allowed to be weakly inhomogeneous in the z-direction. Application is made of the theory to the simple equilibrium case as a test yields the Rayleigh-Jeans formula of the black-body-radiation.     

Nonapplicability of the viscous approximation method in homogeneous cosmological models

By considering two conceptually important instances it is shown that one cannot use the viscous approximation method to estimate the effects of nonequilibrium processes in homogeneous cosmological models. Despite the widespread acceptance of this method, it is argued that not even qualitative estimates can be obtained by its use.     

Thermodynamic Modeling of Developed Structural Turbulence Taking into Account Fluctuations of Energy Dissipation

A thermodynamic approach to the construction of a phenomenological macroscopic model of developed turbulence in a compressible fluid is considered with regard for the formation of space–time dissipative structures. A set of random variables were introduced into the model as internal parameters of the turbulent–chaos subsystem. This allowed us to obtain, by methods of nonequilibrium thermodynamics, the kinetic Fokker–Planck equation in the configuration space. This equation serves to determine the temporary evolution of the conditional probability distribution function of structural parameters pertaining to the cascade process of fragmentation of large-scale eddies and temperature inhomogeneities and to analyze Markovian stochastic processes of transition from one nonequilibrium stationary turbulent-motion state to another as a result of successive loss of stability caused by a change in the governing parameters. An alternative method for investigating the mechanisms of such transitions, based on the stochastic Langevin-type equation intimately related to the derived kinetic equation, is also considered. Some postulates and physical and mathematical assumptions used in the thermodynamic model of structurized turbulence are discussed in detail. In particular, we considered, using the deterministic transport equation for conditional means, the cardinal problem of the developed approach—the possibility of the existence of asymptotically stable stationary states of the turbulent-chaos subsystem. Also proposed is the nonequilibrium thermodynamic potential for internal coordinates, which extends the well-known Boltzmann–Planck relationship for equilibrium states to the nonequilibrium stationary states of the representing ensemble. This potential is shown to be the Lyapunov function for such states. The relation is also explored between the internal intermittence in the inertial interval of scales and the fluctuations of the energy of dissipation. This study is aimed at constructing representative models of natural space environments. It develops a synergetic approach to modeling the structurized turbulence of astrophysical and geophysical systems, which was proposed by the author in previous papers (Kolesnichenko, 2002, 2003).     

On the boundary conditions on a shock wave for hypersonic flow around a descent vehicle

Stationary hypersonic flow around a descent vehicle is examined by considering equilibrium and nonequilibrium reactions. We study how physical-chemical processes and shock wave conditions for gas species influence the shock-layer structure. It is shown that conservation conditions of species on the shock wave cause high-temperature and concentration gradients in the shock layer when we calculate spacecraft deceleration trajectory in the atmosphere at 75 km altitude.     

Stability of thermonuclear reaction affected by gravitational force

A reaction-diffusion equation describing thermonuclear reaction system affected by gravitational force and temperature gradient is obtained by using the theory of nonequilibrium thermodynamics. We take CNO cycle as an example to investigate the effects of the gravitional force and temperature gradient on the stability of nuclear reaction inside the star. The stability criterion of the stellar structure has been analysed and some attractive results have also been discussed.     

Dynamical behavior of nuclear reaction systems disturbed by fluid motion in the solar core

Using Euler's equation of motion, the equation for disturbed fluid motion against a hydrostatic equilibrium has been derived, and the nonequilibrium dynamical equation of a P-PI nuclear reaction system driven by He³ has been analysed using developed nonequilibrium theory. We find that the system in the solar core is unstable in the layer extending from about 0.2R to 0.4R if the core is disturbed by fluid motion; this instability may be related to thermal diffusion.     

Accretion and evolution in close binaries

The discovery of X-ray binary systems in the 1960's opened up stellar evolution theory by revealing further endpoints in addition to white dwarfs. This review summarises recent progress in studies of stellar-evolutionary processes that lead to X-ray binaries themselves, the mass transfer rates that power them, and the accretion processes which convert this into electromagnetic radiation. Particular attention is paid to the topics of mass transfer fluctuations and of the accretion by magnetic compact stars.     

Nonequilibrium Radiative Hypersonic Flows: Aerospace Applications

Hyperenthalpic flows are encountered when spatial vehicules reenter the atmosphere (Anderson 1989) or in some astrophysical situations as in envelopes of cool pulsating stars (Lafon 1991). In reentry applications, a bow shock is created at the front of the vehicule. The plasma in the shock layer is highly collisional and the radiative heat flux is of the same order of magnitude as the convective heat flux. It is then necessary to take into account the coupling between aerodynamics and radiation. For high mach numbers, electronic collisional processes are out of equilibrium, and each atomic electronic level has to be considered as a distinct chemical species. The structure of the system is globally non-linear and the coupling is taken into account by mass conservation, energy exchange, and radiation-matter interaction. The radiative transfer also depends on atomic and molecular spectra in conditions of nonequilibrium for which cross sections and reaction rates are not well known and difficult to calculate. This revised version was published online in July 2006 with corrections to the Cover Date.     

Spectropolarimetric modelling of hot star wind structure

A short overview is given of some recent progress in the theory of spectropolarimetry as a diagnostic of axisymmetric hot star wind density and velocity structure, covering the inferences possible from broad band polarimetry, from polarimetric light curves and simultaneous absorption line data, and from spectropolarimetric line profiles. Recent work on joint spectro-, photo-, and polari-metric study of the properties of wind inhomogeneities is also summarised. One of the most important conclusions is that the blobs necessary in WR winds to produce narrow emission line features cannot also produce polarimetric light curve features unless they originate in enhanced mass loss sources at the stellar surface rather than solely in density redistribution processes, such as turbulence, in the wind itself.     

Dynamical equation for the degree of ionization of the cosmic substratum before the formation of the galaxy

We discuss the variable degree of ionizationx of a hydrogen-helium plasma in the early Universe for a quasi-static expansion in thermal equilibrium. The final equation for the degree of ionization can be reduced to a polynomial of fourth order inx with known coefficients depending on the temperature. Restricting to a pure hydrogen-plasma applied to the recombination era, where the main ionization effects are due to photo-electric and collisional processes, we study the dynamical evolution of the degree of ionization for nonstatic and nonequilibrium situations. The calculation can be reduced to a pure quadrature. In the linear case, we also calculate the rate of ionization.     

Nonequilibrium carbon ionization states and the extragalactic far-UV background with HeII absorption

Using nonequilibrium calculations of the ionic states and the recently calculated extragalactic ultraviolet background radiation with absorption by intergalactic HeII we determine the ratios of CIII to CIV expected at z∼2–3, as functions of metallicity, gas density and temperature. We constrain the spectrum of the extragalactic ultraviolet background radiation by fitting the observed abundance ratios carbon ions at these redshifts with those expected from different models of the background radiation. Our analysis of the observed ratios shows that ‘delayed reionization’ models, which assume a large fraction of HeII at z∼3, is not favored by data. Our results suggest that HeII reionization was inhomogeneous, consistent with the predictions from recent simulations.     

Topological stability of finite-length magnetic flux tubes

It has been suggested that the activity of cosmical magnetic fields is a consequence of a general topological nonequilibrium in the neighbourhood of magnetostatic equilibria. Evidence for this suggestion can be obtained from the Kolmogorov-Arnold-Moser theorem of classical mechanics, applied to the magnetic field line flow as a Hamiltonian system. A finite-length magnetic flux tube, however, always possesses two independent sets of flux surfaces - or, equivalently, the corresponding Hamiltonian system two independent first integrals - and is topologically stable if in the volume occupied by the tube there are no singular (null) points of the magnetic field and the normal field component does not change its sign on the end faces of the tube. Therefore, the concept of nonequilibrium due to flux surface destruction is not applicable to solar atmospheric loops with each end situated in the interior of one polarity of the photospheric normal field component. Further, it seems unlikely that the tearing-mode mechanism can play a role in such loops.     

What Does the Nonextensive Parameter Stand for in Self-Gravitating Systems?

It is natural important question for us to ask what the nonextensive parameter stands for when Tsallis statistics is applied to the self-gravitating systems. In this paper, some properties of the nonextensive parameter and Tsallis’ equilibrium distribution for the self-gravitating system are discussed in the framework of nonextensive kinetic theory. On the basis of the solid mathematical foundation, the nonextensive parameter can be expressed by a formula with temperature gradient and the gravitational potential and it can be related to the non-isothermal (nonequilibrium stationary state) nature of the systems with long-range interactions. We come to the conclusion that Tsallis’ equilibrium distribution is corresponding to the physical state of self-gravitating system at the hydrostatic equilibrium. PACS numbers 05.20.-y, 95.30.Lz     

Computer simulation of chemical nucleation

The problem of nucleation at chemical instabilities is investigated by means of microscopic computer simulation. The first-order transition of interest involves a new kind of nucleation arising from chemical transformations rather than physical forces. Here it is the chemical state of matter, and not matter itself, which is spatially localized to form the nucleus for transition between different chemical states. First, the concepts of chemical instability, nonequilibrium phase transition, and dissipative structure are reviewed briefly. Then recently developed methods of reactive molecular dynamics are used to study chemical nucleation in a simple model chemical reaction. Finally, the connection of these studies to nucleation and condensation processes involving physical and chemical interactions is explored.Invited contribution to the Proceedings of a Workshop onThermodynamics and Kinetics of Dust Formation in the Space Medium held at the Lunar and Planetary Institute, Houston, 6–8 September, 1978.     

Nuclear fission in the neutron stars andγ-ray bursts

Nuclear explosions near the surface of a neutron star occur because of the nuclear fission of superheavy nuclei which is overabundant in neutrons. Such nuclei exist in the nonequilibrium layer of the neutron stars solid envelope and are transported close to the surface in starquake events. These explosions may be observed as γ-ray bursts.