Nonequilibrium statistical thermodynamics of channeled particles: Thermal particles

The rate of atomic particles escaping a potential minimum as a result of interactions with the lattice thermal vibrations and the electron gas is investigated using nonequlibrium statistical thermodynamic methods. The physical properties of the theory are analyzed. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 116, No. 3, pp. 442–455, September, 1998.     

Nonequilibrium statistical thermodynamics of channeled particles: Resonance transitions and dechanneling

An elementary act of dechanneling includes diffusion of particles in the space of transverse energies and a resonance transition that occurs after a particle reaches the channeling-regime potential level. The dechanneling rate coefficient is defined using equations of nonequilibrium statistical thermodynamics. Physical quantities including the resonance transition matrix element, single-phonon and electron scattering relaxation rates, and the transverse quasi-temperature function related to the difference between the thermodynamic parameters of fast particles and the thermostat determining the dechanneling rate coefficient are expressed in terms of the basic parameters of the theory. Translated from Teoreticheskaya i Matematicheskaya Fizika. Vol. 116, No. 1, pp. 146–160, July, 1998.     

Dependence of equilibrium properties of channeled particles on the transverse quasitemperature

We use methods of nonequilibrium thermodynamics to investigate the quasiequilibrium and kinetic characteristics of channeled particles regarded as a separate thermodynamic subsystem. For the channeled particles, we derive the energy—momentum balance equation in the moving coordinate system and show that the solution of the balance equation provides an expression for the main thermodynamic parameter, the transverse quasitemperature of the channeled-particle subsystem. We study the quasiequilibrium angular distribution of particles after their passage through a thin single crystal, the quasiequilibrium distribution over the particle exit angles under backscattering conditions, and also the rate constant for the nonequilibrium (dechanneling) process at large deviations of the system as a whole from the thermodynamic equilibrium. We discuss a measurement method for the particle beam transverse temperature over the peak height of the angular particle distribution found in the framework of a “shoot-through” experiment. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 3, pp. 509–524, March, 2006.     

Balance equation and the quasitemperature of channeled particles in equilibrium

Using the methods of nonequilibrium statistical thermodynamics, we obtain the equation for the transverse energy and momentum balance for fast atomic particles moving in the planar channeling regime. Based on the solution of this equation, we obtain an expression for the transverse quasitemperature in the quasiequilibrium in terms of the basic parameters of the theory. We show that the equilibrium quasitemperature of channeled particles is established because of particle diffusion in the space of transverse energies (subsystem “heating”), the dissipative process (“cooling”), and the anharmonic effects of particle oscillations between the channel walls (the redistribution of energies over the oscillatory degrees of freedom is the internal thermalization of the subsystem). According to the estimates for particles with an energy of the order of 1 MeV, the quasitemperature values are in the characteristic temperature range for a low-temperature plasma.     

The second law of thermodynamics for high-energy channeled particles

In microscopic theory, the number of kinetic equations underlying the proof of the second law of thermodynamics is quite restricted. We explicitly prove that the second law of thermodynamics is satisfied for high-energy particles moving in a crystal in the channeling regime. The proof involves a local Boltzmann equation for the distribution function of the particles written in the Bogoliubov form. In this, we take one statistical mechanism into account: the scattering of channeled particles on lattice atoms randomly displaced from the crystal sites.     

Nonequilibrium statistical thermodynamics of cascade processes in solids: the quasi temperature of cascade particles

Displacement cascades in solids are investigated in the framework of nonequilibrium statistical thermodynamics. The quasi temperature of a subsystem of cascade particles in metals and semiconductors is derived using the energy balance equation for a cascade process.     

Nonequilibrium statistical thermodynamics of positronium atoms moving in solids

We calculate the quasitemperature of positronium atoms moving in a solid in the framework of nonequilibrium statistical thermodynamics. We represent the quasitemperature in the form of the renormalized temperature of the thermostat. The renormalization results from taking the positronium formation rate, the kinetic effects of interaction, and the dynamical effects of collisions into account. We obtain an expression for the thermalization time of positronium atoms.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 1, pp. 112–126, January, 2005.     

Nonequilibrium statistical thermodynamics of displacement cascade thermalization in a solid

A. A. Baikov Institute of Metallurgy, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 87, No. 2, pp. 283–292, May, 1991.     

Nonequilibrium statistical mechanics of a solid immersed in a continuum

We study actions of the symmetric group S₄ on K3 surfaces X that satisfy the following condition: there exists an equivariant birational contraction \(\bar r:X \to \bar X\) to a K3 surface \(\bar X\) with ADE singularities such that the quotient space \(\bar X\)/S₄ is isomorphic to P². We prove that up to smooth equivariant deformations there exist exactly 15 such actions of the group S₄ on K3 surfaces, and that these actions are realized as actions of the Galois groups on the Galoisations \(\bar X\) of the dualizing coverings of the plane which are associated with plane rational quartics without A₄, A₆, and E₆ singularities as their singular points.     

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. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 1, pp. 91–101, January, 2008.     

Nonequilibrium thermodynamics of a gas of solitons of kink type in quasione-dimensional systems

Institute of Metal Physics, Ukrainian SSR Academy of Sciences, Kiev. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 74, No. 1, pp. 46–60, January, 1988.     

A quantum generalization of equilibrium statistical thermodynamics: Effective macroparameters

We propose a generalization of statistical thermodynamics in which quantum effects are taken into account on the macrolevel without explicitly using the operator formalism while traditional relations between the macroparameters are preserved. In a generalized thermostat model, thermal equilibrium is characterized by an effective temperature bounded from below. We introduce fundamental theoretical macroparameters: the effective entropy and the effective action. Because the effective entropy is nonzero at low temperatures, we can write the third law of thermodynamics in the form postulated by Nernst. The effective action at any temperature coincides with the product of standard deviations of the coordinate and momentum in the Heisenberg uncertainty relation and is therefore bounded from below. We establish that the ratio of the effective action to the effective entropy in the low-temperature limit is determined by a holistic stochastic-action constant depending on the Planck and Boltzmann constants. We show that the same results can be obtained in the framework of a modified version of thermofield dynamics in which the quantum oscillator is described by a temperature-dependent complex macroscopic wave function. We study the discrepancy between the behavior of the action-to-entropy ratio in the low-temperature limit in our proposed theory and that in quantum equilibrium statistical mechanics, which can be verified experimentally. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 1, pp. 183–196, January, 2008.