Classical Representation of a Quantum System at Equilibrium

A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce the thermodynamic and structural properties. The objective is to develop a means for exploiting strong coupling classical methods (e.g., MD, integral equations, DFT) to describe quantum systems. The classical system has an effective temperature, local chemical potential, and pair interaction that are defined by requiring equivalence of the grand potential and its functional derivatives with respect to the external and pair potentials for the classical and quantum systems. Practical inversion of this mapping for the classical properties is effected via the hypernetted chain approximation, leading to representations as functionals of the quantum pair correlation function. As an illustration, the parameters of the classical system are determined approximately such that ideal gas and weak coupling RPA limits are preserved (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Response function theory for far-from-equilibrium statistical systems

A formalism to determine the response function of a sample in conditions far from thermal equilibrium is presented. It consists in a generalization of scattering theory coupled to the statistical theory of irreversible processes, the nonequilibrium statistical operator method, developed by Zubarev. The scattering cross section is expressed in terms of double-time correlation functions, which are related to appropriate nonequilibrium thermodynamic Green's functions. The latter are also used to treat generalized transport equations, and, as an illustration, the method is applied to the study of the time-resolved Raman spectroscopy of a photoexcited semiconductor plasma.     

Real-time kadanoff-baym approach to plasma oscillations in a correlated electron Gas

A nonequilibrium Green's functions approach to the collective response of correlated Coulomb systems at finite temperatures is presented. It is shown that solving Kadanoff-Baym-type equations of motion for the two-time correlation functions including the external perturbing field allows one to compute the plasmon spectrum with collision effects in a systematic and consistent way. The scheme has a "built-in" sum-rule preservation and is simpler to implement numerically than the equivalent equilibrium approach based on the Bethe-Salpeter equation.     

Yang-Lee zeros for an urn model for the separation of sand

We apply the Yang-Lee theory of phase transitions to an urn model for the separation of sand. The effective partition function of this nonequilibrium system can be expressed as a polynomial of the size-dependent effective fugacity z. Numerical calculations show that in the thermodynamic limit the zeros of the effective partition function are located on the unit circle in the complex z plane. In the complex plane of the actual control parameter, certain roots converge to the transition point of the model. Thus, the Yang-Lee theory can be applied to a wider class of nonequilibrium systems than those considered previously.     

Thermodynamic design data for double effect absorption heat pump systems using water-lithium chloride—cooling

In this paper, thermodynamic design data are investigated for the water-lithium chloride pair and a comparative study of the water-LiCl pair with the water-LiBr pair is given, for double-effect absorption cooling systems used for the computer simulation. The computer simulation is based on mass, material and heat balance equations for each part of the system. Coefficients of performance and flow ratios for effects of different operating temperatures are investigated. It is found that the cooling COP is higher for the water-LiCl pair than for the water-LiBr pair, and FR is lower for the water-LiCl pair than for the water-LiBr pair.     

Thermodynamic design data for absorption heat pump systems operating on water-lithium chloride—Part one. Cooling

The free choice of operating temperatures in absorption systems is limited by the Gibbs phase rule and the thermodynamic properties of the working pair. For a given combination of temperatures, the concentrations in the absorber and the generator are fixed automatically. This determines the flow ratio. Therefore for any particular working pair, the coefficient of performance is related to the flow ratio.Tables of possible combinations of operating temperatures and concentrations, including flow ratios, Carnot coefficients of performance and enthalphy based coefficients of performance have been presented for a water-lithium chloride absorption system for cooling. The interaction of operating temperatures has been illustrated graphically. The data obtained are also compared with published data for the water-lithium bromide absorption system under identical conditions.     

The existence of thermodynamic constants characterizing the properties of substances and materials in spontaneous processes

The equations of nonequilibrium thermodynamics show that one of the higher time derivatives of the maximum thermodynamic work remains constant along the trajectory of a spontaneous process. The theoretical prediction is confirmed by experimental data on mechanical motion with friction. The constant characterizing the friction process is called the coefficient of thermodynamic friction losses (KTL). In contrast to the friction coefficient in mechanics, the KTL does not depend on the velocity and acceleration of relative motion of parts of the frictional pair on the trajectory of spontaneous slowing down. The KTL may be regarded as a nonequilibrium thermodynamic parameter specifying at a given temperature the properties of materials involved in the friction process. The usefulness and advantages of utilizing the KTL in engineering computations are noted.Moscow Institute of Chemical Machine Construction. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 58–61, May, 1992.     

On a kinetic justification of the generalized nonequilibrium thermodynamics of multicomponent systems

The problem of the kinetic justification of the generalized thermodynamics of nonequilibrium processes using the method of moments for solving the kinetic equation for a multicomponent gas mixture is examined. Generalized expressions are obtained for the entropy density, entropy flux density, and entropy production as functions of an arbitrary number of state variables (moments of the distribution function). Different variants of writing the relations between fluxes and thermodynamic forces are considered, which correspond to the Onsager version for spatially homogeneous systems and, in a more general case, lead to the generalized thermodynamic forces of a complicated form, including derivatives of the fluxes with respect to time and spatial coordinates. Some consequences and new physical effects, following from the obtained equations, are analyzed. It is shown that a transition from results of the method of moments to expressions for the entropy production and the corresponding phenomenological relations of the generalized nonequilibrium thermodynamics is possible on the level of a linearized Barnett approximation of the Chapman–Enskog method.     

Fokker-Planck equation approach to fluctuations about nonequilibrium steady states

We examine the properties of steady states in systems which interact at the boundary with a nonequilibrium environment. The examination is based on a nonlinear Fokker-Planck equation, the structure of which is determined by the fact that it also governs the time evolution of the equilibrium fluctuations of the system. The nonlinearities in the Fokker-Planck equation may have two origins: thermodynamic nonlinearities which arise if the thermodynamic potential is not a bilinear function of the state variables, and nonlinear mode coupling which arises if the transport coefficients depend on the state. While these nonlinearities have only a small effect on the equilibrium fluctuations of a system away from critical points, they are shown to be important for the determination of fluctuations about nonequilibrium steady states. In particular the state dependence of the transport coefficients may lead to deviations from local equilibrium and to a breakdown of detail balance. An explicit formula for the time correlations of fluctuations about the nonequilibrium steady state is obtained. The formula leads to long-range correlations in fluids in the presence of a temperature gradient. The result is compared with earlier approaches to the same problem. Finally, we study the linear response to external forces and obtain a generalization of the fluctuation-dissipation formula relating the response functions with the nonequilibrium correlation functions.     

Nonequilibrium temperature and fluctuation–dissipation temperature in flowing gases

The expressions for the nonequilibrium temperature derived from the fluctuation–dissipation theorem and from the differential of the informational nonequilibrium entropy for ideal gases under shear flow are compared. Both temperatures are different, in particular, the thermodynamic temperature derived from the entropy is lower than the local-equilibrium temperature, whereas the effective temperature defined from the fluctuation–dissipation expression is higher than the local-equilibrium temperature.     

Thermodynamics of the system benzene-carbon tetrachloride

The thermodynamic behavior of benzene-carbon tetrachloride solutions at temperatures between 30 and 70°C and over the entire concentration range has been examined in terms of the Maron theory of nonelectrolyte solutions. The interaction parameter calculated from vapor pressure data has been found to be independent of concentration and to be linearly dependent on temperature. Use of this parameter in the equations given by the theory allows complete correlation of the available heats, entropies, and heat capacities of mixing for this system. For all these properties very good agreement has been obtained between the calculated and observed quantities.     

Thermodynamics and phase transition of topological dS black holes with a nonlinear source

We discuss black hole solutions of Einstein-Λ gravity in the presence of nonlinear electrodynamics in d S spacetime. Considering the correlation of the thermodynamic quantities respectively corresponding to the black hole horizon and cosmological horizon of dS spacetime and taking the region between the two horizons as a thermodynamic system, we derive effective thermodynamic quantities of the system according to the first law of thermodynamics, and investigate the thermodynamic properties of the system under the influence of nonlinearity parameter α. It is shown that nonlinearity parameter α influences the position of the black hole horizon and the critical state of the system, and along with electric charge has an effect on the phase structure of the system,which is obvious, especially as the effective temperature is below the critical temperature. The critical phase transition is proved to be second-order equilibrium phase transition by using the Gibbs free energy criterion and Ehrenfest equations.     

Photoinduced superstructure in the low-temperature phase of a Peierls system

This paper is a theoretical study of the properties of the low-temperature phase of a Peierls system when nonequilibrium electron-hole pairs are excited in the phase. A microscopic theory is developed to show that at low temperatures a spatially nonuniform periodic structure with a modulated band gap forms in the thermodynamically nonequilibrium system considered. The critical temperature of formation of such a superstructure, the critical electron-hole pair concentration, the spatial period, and the percentage modulation are calculated. Zh. éksp. Teor. Fiz. 115, 1297–1314 (April 1999)     

Statistical mechanics of nonlinear hydrodynamic fluctuations

The paper studies nonlinear hydrodynamic fluctuations by the methods of nonequilibrium statistical mechanics. The generalized Fokker-Planck equation for the distribution function of coarse-grained densities of conserved quantities is derived from the Liouville equation and then is investigated by using the gradient expansions in the flux correlation matrix. We have obtained the functional-differential Fokker-Planck equation describing the nonlinear hydrodynamic fluctuations in spatially nonuniform systems to second order in gradients of coarse-grained fluctuating fields. An outline of the derivation of Fokker-Planck equations containing the Burnett terms is also given. The explicit coordinate representation for the hydrodynamic Fokker-Planck equation is discussed in the case of one-component simple fluid. The general scheme of a change of coarse-grained functional variables is developed for hydrodynamic Fokker-Planck equations. The corresponding transformation rules are found for “drift” terms, “diffusion coefficients” and thermodynamic forces. The dynamical equations and stationary conditions for averages of functions (functionals) of hydrodynamic fields are discussed by using the Fokker-Planck operators acting on such functions. The explicit form of these operators are found for various sets of fluctuating fields. As an application of the formalism the calculation of the stationary correlation functions is presented for a simple nonequilibrium steady state.     

Ground state energy of a many-particle boson system

A trial expression for the ground state energy of a system of many bosons interacting with strong forces is studied. Using an approximate expression for the pair-distribution function and applying the variational principle in an appropriate way, we obtain a non-linear integrodifferential equation for the correlation functionf(r). This equation is subsequently linearised and its behaviour for large separations is studied. It is also shown that for large separations an effective reduced mass of the pair can be defined. This is given by ^*=2, where=m/2 is the reduced mass of the pair.     

Fluids with highly directional attractive forces. II. Thermodynamic perturbation theory and integral equations

The formalism of statistical thermodynamics developed in the preceding paper is used as a basis for deriving tractable approximations. The system treated is one where repulsion and highly directional attraction due to a single molecular site combine to allow the formation of dimers, but no highers-mers. We derive thermodynamic perturbation theory, using the system interacting with only the repulsive potential as a reference system. Two distinct integral equations for the pair correlation are derived. The first one treats both parts of the interaction approximately; the other one employs the repulsive reference system used in perturbation theory. We show that each of these integral equations permits the calculation of an important thermodynamic function directly from the solution at a single state of density and temperature. In the first case this applies to a pressure consistent with the compressibility relation, in the second to the excess Helmholtz free energy over the reference system.Supported by the NSF under Grant No. CHE-82-11236 and by the U.S. Air Force under Grant No. AFOSR 82-0016A.