Fluctuation-Dissipation Rellations for Equilibrium and Non-Equilibrium States. Kinetic Equations for Many-Particle Distribution Functions

1984 ◽  
Vol 24 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Yu. L. Klimontovich
Keyword(s):  
Particle Distribution ◽  
Kinetic Equations ◽  
Distribution Functions ◽  
Equilibrium States ◽  
Fluctuation Dissipation ◽  
Non Equilibrium

Reply to ‘Comment on “Collective effects in bremsstrahlung in plasmas” ’

1998 ◽  
Vol 60 (2) ◽  
pp. 447-448 ◽  
Author(s):  
V. N. TSYTOVICH ◽  
R. BINGHAM ◽  
U. de ANGELIS ◽  
A. FORLANI
Keyword(s):  
Particle Distribution ◽  
Thermal Plasmas ◽  
Solar Interior ◽  
The Other ◽  
Standard Approach ◽  
Collective Effects ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
Electron Bremsstrahlung ◽  
Non Equilibrium

We reply here to a criticism of our paper (Tsytovich et al. 1996) by Iglesias (1997).In our paper we present a very general formulation of collective effects in bremsstrahlung that is valid for any non-equilibrium non-Maxwellian particle distribution. This result is given in (2.20) early in the paper. The standard treatments of bremsstrahlung found in books like Bekefi (1966) are only for thermal plasmas, where the fluctuation–dissipation theorem is valid. Note that the fluctuation–dissipation theorem cannot be used for non-thermal or non-dipole fields, and in this respect the method we use is more general. Our method is the more complex of the approaches used, but, as stated, it can handle situations that cannot be treated by the standard approach. Our main result is the formula (2.20), which is valid for any non-equilibrium non-Maxwellian particle distribution, and which cannot be found anywhere else in the literature. Furthermore, we find new qualitative effects indicating that the ion–ion bremsstrahlung (which is always neglected in the literature) is not small in the case where the collective effects are taken into account, and is in fact, for certain frequencies, of the order of the electron–electron bremsstrahlung. The other qualitatively new result is that, where collective effects are important, the electron–electron bremsstrahlung is not of the order v2Te/c2, as it is for the case in the absence of collective effects, but of the order ω2pe/ω2 times less – which, for example in the solar interior, where ω2pe/ω2 is of the order of v2Te/c2, is then of the order of v4Te/c4.

Kinetic theory of a spatially inhomogeneous plasma with time independent average properties

1970 ◽  
Vol 4 (1) ◽  
pp. 51-65 ◽  
Author(s):  
R. A. Cairns
Keyword(s):  
Particle Distribution ◽  
Inhomogeneous Plasma ◽  
Kinetic Equations ◽  
Distribution Functions ◽  
Plane Shock ◽  
Infinite Plane ◽  
Fluctuation Spectrum ◽  
Field Fluctuation ◽  
Spatial Direction ◽  
Spatially Inhomogeneous

Kinetic equations are obtained which describe the variation in one spatial direction of a plasma whose average properties are independent of time and do not vary in the perpendicular direction.These equations consist of a coupled set giving the variation of the electric field fluctuation spectrum and the particle distribution functions. They take into account particle discreteness effects and describe the plasma both when it is stable and weakly unstable. It is suggested that they may be used to describe an infinite plane shock wave in a plasma.

Thermodynamics and foundations of mass-action kinetics

2005 ◽  
Vol 30 (1-2) ◽  
pp. 3-113 ◽  
Author(s):  
Miloslav Pekař
Keyword(s):  
Chemical Kinetics ◽  
Reaction Rate ◽  
Chemical Potential ◽  
Kinetic Equations ◽  
Reaction Rates ◽  
Equilibrium States ◽  
Mass Action ◽  
Rate Equations ◽  
Mass Action Kinetics ◽  
Non Equilibrium

A critical overview is given of phenomenological thermodynamic approaches to reaction rate equations of the type based on the law of mass-action. The review covers treatments based on classical equilibrium and irreversible (linear) thermodynamics, extended irreversible, rational and continuum thermodynamics. Special attention is devoted to affinity, the applications of activities in chemical kinetics and the importance of chemical potential. The review shows that chemical kinetics survives as the touchstone of these various thermody-namic theories. The traditional mass-action law is neither demonstrated nor proved and very often is only introduced post hoc into the framework of a particular thermodynamic theory, except for the case of rational thermodynamics. Most published “thermodynamic'’ kinetic equations are too complicated to find application in practical kinetics and have merely theoretical value. Solely rational thermodynamics can provide, in the specific case of a fluid reacting mixture, tractable rate equations which directly propose a possible reaction mechanism consistent with mass conservation and thermodynamics. It further shows that affinity alone cannot determine the reaction rate and should be supplemented by a quantity provisionally called constitutive affinity. Future research should focus on reaction rates in non-isotropic or non-homogeneous mixtures, the applicability of traditional (equilibrium) expressions relating chemical potential to activity in non-equilibrium states, and on using activities and activity coefficients determined under equilibrium in non-equilibrium states.

scholarly journals Неравновесная кинетика начальной стадии фазового перехода

2020 ◽  
Vol 62 (1) ◽  
pp. 40
Author(s):  
Г.И. Змиевская
Keyword(s):  
Phase Transition ◽  
Transition Probability ◽  
Kinetic Equations ◽  
Elastic Interaction ◽  
Distribution Functions ◽  
Condensation Process ◽  
Stochastic Dynamic ◽  
Transition Probability Density ◽  
Temporal Structures ◽  
Non Equilibrium

Kinetic partial differential equations of Kolmogorov-Feller and Einstein-Smoluchowski equation with nonlinear coefficients are solved by a new, stable numerical methods. The theory of stochastic dynamic variables establishes the connection of the solution of Ito stochastic equations in the sense of Stratonovich for the trajectories of Wiener random processes with the transition probability density of these processes, or distribution functions of kinetic equations. The classical theory of nucleation (formation of nuclei of the first order phase transition) describes a non-equilibrium stage of the condensation process by a diffusion random process in the space of the size of the nuclei of the phase transition, when fluctuations affect the clustering of the nuclei. The model of formation of vacancy-gas defects (pores, blisters) in the crystal lattice, arising as a result of its irradiation by inert gas ions xenon, is supplemented by the consideration of Brownian motion of non-point lattice defects, occurring under the action of superposition of paired long-range potentials of indirect elastic interaction of pores between themselves and with the boundaries of the layers. Pores coordinates are changing at times of the order of 10 − 100 ms, sustainable algorithms for calculating which provide a self-consistent defnition spatial - temporal structures of porosity in the sample. According to calculations of 106 trajectories, non-equilibrium kinetic functions were found. Pores distribution in size and coordinates in the layers of the irradiated materials, they characterize the fluctuation instability the initial stage of the phase transition, they are estimated local stresses and porosity in the model volume.

scholarly journals Quantum Current Algebra Symmetry and Description of Boltzmann Type Kinetic Equations in Statistical Physics

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1452
Author(s):  
Lev Ivankiv ◽  
Yarema Prykarpatsky ◽  
Valeriy Samoilenko ◽  
Anatolij Prykarpatski
Keyword(s):  
Current Algebra ◽  
Statistical Physics ◽  
Particle Distribution ◽  
Particle System ◽  
Kinetic Equations ◽  
Distribution Functions ◽  
Kinetic Properties ◽  
Particle Correlation ◽  
Symmetry Approach ◽  
Dual Analysis

We review a non-relativistic current algebra symmetry approach to constructing the Bogolubov generating functional of many-particle distribution functions and apply it to description of invariantly reduced Hamiltonian systems of the Boltzmann type kinetic equations, related to naturally imposed constraints on many-particle correlation functions. As an interesting example of deriving Vlasov type kinetic equations, we considered a quantum-mechanical model of spinless particles with delta-type interaction, having applications for describing so called Benney-type hydrodynamical praticle flows. We also review new results on a special class of dynamical systems of Boltzmann–Bogolubov and Boltzmann–Vlasov type on infinite dimensional functional manifolds modeling kinetic processes in many-particle media. Based on algebraic properties of the canonical quantum symmetry current algebra and its functional representations, we succeeded in dual analysis of the infinite Bogolubov hierarchy of many-particle distribution functions and their Hamiltonian structure. Moreover, we proposed a new approach to invariant reduction of the Bogolubov hierarchy on a suitably chosen correlation function constraint and deduction of the related modified Boltzmann–Bogolubov kinetic equations on a finite set of multi-particle distribution functions. There are also presented results of application of devised methods to describing kinetic properties of a many-particle system with an adsorbent surface, in particular, the corresponding kinetic equation for the occupation density distribution function is derived.

THE RELAXATION THEORY OF ELECTROELASTICITY AND DIELECTRIC PROPERTIES OF IONIC LIQUIDS

2001 ◽  
Vol 15 (09n10) ◽  
pp. 285-290 ◽  
Author(s):  
S. ODINAEV ◽  
I. ODJIMAMADOV
Keyword(s):  
Ionic Liquids ◽  
Dielectric Properties ◽  
Particle Distribution ◽  
Kinetic Equations ◽  
Distribution Functions ◽  
Relaxation Processes ◽  
Dynamic Coefficient ◽  
Relaxation Theory ◽  
High Frequencies ◽  
Electroelasticity Modulus

An analytic dynamic coefficient of electroconductivity σ(ω) and electroelasticity modulus ε(ω) for ionic liquids is obtained from the kinetic equations for one- and two-particle distribution functions. These expressions include both structural and translational relaxation processes which proceed in the ionic liquids. An asymptotic behavior of σ(ω) and corresponding ∊(ω) at low and high frequencies is considered. It is shown that the obtained results for electroconductivity allow us to investigate dielectric properties of ionic liquids.

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