The thermodynamic properties of hard-rod fluids confined to a plane are derived using scaled particle theory, and restricting the number of possible orientations to six. Results for simple systems are compared with earlier results for three-dimensional spherocylindrical systems. Mixtures of rods of different lengths are also studied as possible models for systems in which the constituent molecules may change conformation. Upon inclusion of a van der Waals attractive potential energy, interesting and unusual phase changes can occur.

We compute the internal energy of the classical one-component plasma, for values of the Coulomb coupling parameter $\Gamma$ between 1 and 300, by using converged Monte Carlo chains and a more accurate potential approximation than that used by Hansen. The liquid data are fitted to a simple, very accurate four-parameter formula from which the Helmholtz free energy is derived. The solid data are likewise fitted to a one-parameter formula. The intersection of the two free-energy curves gives an estimate of the fluid-solid transition at $\Gamma =168\mathrm{}\pm 4$.

A new interpretation of the tungsten spectrum observed in 1.5-keV tokamak plasmas at Oak Ridge (the ORMAK) and Princeton (the PLT) is given. An isoelectronic extrapolation of the Agi sequence from newly observed data through Hoxxi strongly suggests that the tokamak radiation belongs to the transition array $4d^{10}4f-4d^{9}4f^2$ of Wxxviii. This is well supported by comparison with a calculation of the spectrum. An earlier interpretation incorrectly attributed the radiation to a superposition of complex transition arrays from much higher ionization stages.

A Landau-Ginzburg-Wilson model is derived for a single-component fluid whose particles interact via a two-body potential. The effective Hamiltonian contains both even and odd powers in the order parameter (local fluid density). We study the effect of quintic interactions absent in the Ising model, and characterized by a new exponent ${\phi }_5$, on various singular thermodynamic functions near the critical point. Mean-field, scaling, and renormalization-group (in $d=4-\epsilon$ dimensions) theories are used to evaluate the non-Ising effects due to ${\phi }_5$. One of the main results of the asymmetry in this model is that it produces the leading singularity of the liquid-vapor coexistence diameter near the critical point: ${\mathrm{}\left|t\right|\mathrm{}}^{\beta -{\phi }_5}$, where $\beta$ is the usual order-parameter exponent and $t$ is the reduced tem$\stackrel{\mathrm{̇}}{\mathrm{p}}$erature. The singularity ${\mathrm{}\left|t\right|\mathrm{}}^{1-\alpha }$ ($\alpha$ being the specific heat exponent) predicted by earlier phenomenological theories is not present in this theory. The problems associated with observing the non-Ising effects are briefly discussed.

We consider the problem of minimum entropy production in a heat engine subject only to thermal-resistance losses. For such engines, minimizing the total entropy production is equivalent to minimizing the loss of availability. We show for any engine operating with a given cycle time that minimum total entropy production is achieved in a heat engine by operating it so as to keep the entropy production rate constant along each branch. For the limit of slow engine operation, the entropy production rate should be the same constant for all branches of the cycle. We obtain an expression for the minimum total entropy production and use this to give a bound on the maximum work which can be produced by such engines. This bound is significantly more realistic than the reversible one. Analogous results are derived for a working fluid which carries arbitrary flows from one potential to another.

We investigate the nonequilibrium properties of $N$ classical point particles on a ring at finite density; the dynamics consists of a velocity-dependent probability of penetration. In particular, we determine the self-distribution function of a labeled test particle. The long-time behavior is exhibited for both normal diffusive behavior and for anomalous "diffusion." Implications for the frequency-dependent conductivity are discussed.

This paper forms the second part of a study which reexamines the relationship between fluctuations and nonlinear irreversible processes. The scope of the previous paper is generalized to include macroscopic variables which transform odd under time reversal. The fluxes of some of the variables may be purely reversible so that the diffusion matrix may be singular. The deterministic equations for nonlinear irreversible processes can again be derived from a minimum principle. The fluctuations of the macroscopic variables are treated on the basis of a Fokker-Planck equation which has the form derived from statistical mechanics by one of us. The conditional probability of the fluctuations is constructed as a path integral. The connection between the deterministic and the stochastic descriptions of the macroscopic dynamics is formulated in a covariant way, independent of the frame of coordinates. For that purpose, a metric tensor in the space of state variables is introduced. The form of the metric tensor is particularly simple in frames where the macroscopic variables are sums of molecular variables.

This paper is concerned with the derivation of nonlinear fluctuation-renormalized transport equations of a fluctuating thermodynamic system, on the assumption that the macroscopic variables defining a state undergo a Fokker-Planck process. It is shown that the renormalization effect may consist of two parts: a renormalization of the thermodynamic forces and a renormalization of the transport coefficients. Closed analytical expressions for the renormalized quantities in terms of the bare quantities appearing in the Fokker-Planck equation are derived. A scheme for the approximate evaluation of these expressions is given.

In this paper the method of Robertson and that of Zubarev, which have been applied to isolated systems, are modified by using a special projection operator or a special density operator so that they become applicable to open systems. As a result, exact equations are obtained in the form of coupled integro-differential equations with expectation values corresponding to a set of operators of an open system $S$ as the only unknowns. The variables of the system $R$, which interacts with the system $S$, are completely eliminated up to the expectation values taken over the initial state of $R$. The differences between the above mentioned two methods are discussed. It is shown that for special choice of the initial conditions, sets of operators and properties of system $R$, significant simplifications of the equations of motion can be made. Moreover, an expansion of the equations of motion in powers of the interaction and an approximation of the second order are made. Finally, a Kawasaki-Gunton modification of our projection operator is made in the Appendix.

The recent theory of Raedt and Raedt (RR) is analyzed and applied to study the dynamics of a classical one-component plasma. It is shown that this method is very similar to making the Lovesey approximation (for the calculation of the memory function involved) at an appropriate stage of the continued fraction hierarchy for the memory function. The expression for the density-fluctuation spectrum obtained by using RR theory is then evaluated for the entire density range for which molecular dynamics data are available. For smaller $q$ values the results obtained are of similar quality to those obtained recently by this author using a renormalized free-particle memory function, and compare well with the data. However, for larger $q$ values a shoulder appears at high frequencies which is not observed in the molecular-dynamics results.

The measurements of the anomalous effective viscosity $\eta$ obtained by Keyes and coworkers are analyzed in terms of the two separate viscosity coefficients $\nu$ and $\mu$.

The corrected formula for the laser scattering intensity in collision-dominated plasmas is given. Expressions for the ratios of the ion to electron peak intensities and integrated intensities are obtained. These ratios and the intensity profile are compared to experimental data with good agreement.

An approximate analytical treatment of a convergent sequence of imploding shocks is presented within the framework of gas-dynamic equations for self-similar motion. The analytical solutions are compared with the exact numerical solutions for the spherical and cylindrical geometries.

In a previous publication, the motion of a charged particle gyrating in a slowly varying magnetic field was considered, and the existence of an invariant established. The purpose of this note is to exhibit an explicit form for this invariant.

Potential-energy curves for the ${}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ states of ${\mathrm{Ba}}_2^{++}$ are exhibited. The ground-state curve shows a local minimum lying 0.0562 a.u. above the energy at infinite separation, and a local maximum lying at 0.0618. These features form a potential well in which metastable vibrational states can exist. The lifetimes are estimated as high as ${10}^{197}$ sec, using the WKB method. Considerations regarding experimental formation and detection of bound ${\mathrm{Ba}}_2^{++}$ are discussed.

The construction of a potential barrier around an atom such that a chosen zeroth-order reference state is left unaffected results in a square-integrable virtual basis set with rapid convergence properties for use in atomic many-body perturbation theory. Encouraging results have been obtained using this technique for calculations of the correlation energies and transition probabilities of small atoms and ions. In the case of ${\mathrm{H}}^{-}$ it is shown that the conventional formulation of many-body perturbation theory involving continuum functions produces classes of energy diagrams which diverge with order, although the total summation remains finite. No such divergence is present in a properly constructed contracted basis set.

The correlation coefficient which is used in mathematical statistics is evaluated for an exactly soluble electron correlation problem. Our results show that a wave function with a very "negative" correlation coefficient is not necessarily energetically (hence variationally) a good approximation to the exact wave function. We discuss the importance of this result vis-a-vis the notion in the literature that the correlation coefficient provides a useful tool for analyzing approximate wave functions.

Local scaled Schrödinger relationships are derived connecting the potential (assumed homogeneous of degree $q$) and the kinetic-energy operator and also between the total energy and the kinetic-energy operator. The virial relationships that follow from these local equations are derived. A reduced local energy connection between the total energy and the kinetic-energy operator is derived in terms of "scaled one- and two-particle density matrices."