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The methodology developed by Lustig for calculating thermodynamic properties in the microcanonical and canonical ensembles [J. Chem. Phys. 100, 3048 (1994)JCPSA60021-960610.1063/1.466446; Mol. Phys. 110, 3041 (2012)MOPHAM0026-897610.1080/00268976.2012.695032] is applied to derive rigorous expressions for thermodynamic properties of fluids in the grand canonical ensemble. All properties are expressed by phase-space functions, which are related to derivatives of the grand canonical potential with respect to the three independent variables of the ensemble: temperature, volume, and chemical potential. The phase-space functions contain ensemble averages of combinations of the number of particles, potential energy, and derivatives of the potential energy with respect to volume. In addition, expressions for the phase-space functions for temperature-dependent potentials are provided, which are required to account for quantum corrections semiclassically in classical simulations. Using the Lennard-Jones model fluid as a test case, the derived expressions are validated by Monte Carlo simulations. In contrast to expressions for the thermal expansion coefficient, the isothermal compressibility, and the thermal pressure coefficient from the literature, our expressions yield more reliable results for these properties, which agree well with a recent accurate equation of state for the Lennard-Jones model fluid. Moreover, they become equivalent to the corresponding expressions in the canonical ensemble in the thermodynamic limit.

Accurate phase diagrams of multicomponent plasmas are required for the modeling of dense stellar plasmas, such as those found in the cores of white dwarf stars and the crusts of neutron stars. Those phase diagrams have been computed using a variety of standard techniques, which suffer from physical and computational limitations. Here, we present an efficient and accurate method that overcomes the drawbacks of previously used approaches. In particular, finite-size effects are avoided as each phase is calculated separately; the plasma electrons and volume changes are explicitly taken into account; and arbitrary analytic fits to simulation data are avoided. Furthermore, no simulations at uninteresting state conditions, i.e., away from the phase coexistence curves, are required, which improves the efficiency of the technique. The method consists of an adaptation of the so-called Gibbs-Duhem integration approach to electron-ion plasmas, where the coexistence curve is determined by direct numerical integration of its underlying Clapeyron equation. The thermodynamics properties of the coexisting phases are evaluated separately using Monte Carlo simulations in the isobaric semi-grand canonical ensemble. We describe this Monte Carlo-based Clapeyron integration method, including its basic principles, our extension to electron-ion plasmas, and our numerical implementation. We illustrate its applicability and benefits with the calculation of the melting curve of dense C/O plasmas under conditions relevant for white dwarf cores and provide analytic fits to implement this new melting curve in white dwarf models. While this work focuses on the liquid-solid phase boundary of dense two-component plasmas, a wider range of physical systems and phase boundaries are within the scope of the Clapeyron integration method, which had until now only been applied to simple model systems of neutral particles., 18 pages, 14 figures, and 2 tables. Accepted for publication in Phys. Rev. E on 2021-04-01

We explore the performance of the Gibbs-ensemble Monte Carlo simulation technique by calculating the miscibility gap of ${\mathrm{H}}_{2}\text{\ensuremath{-}}\mathrm{He}$ mixtures with analytical exponential-six potentials. We calculate several demixing curves for pressures up to 500 kbar and for temperatures up to $1800\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and predict a ${\mathrm{H}}_{2}\text{\ensuremath{-}}\mathrm{He}$ miscibility diagram for the solar He abundance for temperatures up to $1500\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and determine the demixing region. Our results are in good agreement with ab initio simulations in the nondissociated region of the phase diagram. However, the particle number necessary to converge the Gibbs-ensemble Monte Carlo method is yet too large to offer a feasible combination with ab initio electronic structure calculation techniques, which would be necessary at conditions where dissociation or ionization occurs.

For a noisy spin system, we derive a nonlocal stochastic version of the overdamped Landau-Lipshitz equation designed to respect the underlying Hamiltonian structure and sample the canonical or Gibbs distribution while being driven by spatially correlated (colored) noise that regularizes the dynamics, making this Stochastic partial differential equation mathematically well-posed. We begin from a microscopic discrete-time model motivated by the Metropolis-Hastings algorithm for a finite number of spins with periodic boundary conditions whose values are distributed on the unit sphere. We thus propose a future state of the system by adding to each spin colored noise projected onto the sphere, and then accept this proposed state with probability given by the ratio of the canonical distribution at the proposed and current states. For uncorrelated (white) noise this process is guaranteed to sample the canonical distribution. We demonstrate that for colored noise, the method used to project the noise onto the sphere and conserve the magnitude of the spins impacts the equilibrium distribution of the system, as coloring projected noise is not equivalent to projecting colored noise. In a specific scenario we show this break in symmetry vanishes with vanishing proposal size; the resulting continuous-time system of Stochastic differential equations samples the canonical distribution and preserves the magnitude of the spins while being driven by colored noise. Taking the continuum limit of infinitely many spins we arrive at the aforementioned version of the overdamped Landau-Lipshitz equation. Numerical simulations are included to verify convergence properties and demonstrate the dynamics.

Considered is a generalized Gibbs ensemble of the classical Toda lattice. We establish that the collision rate ansatz follows from (i) the charge-current susceptibility matrix is symmetric and (ii) the stretch current is proportional to the momentum, hence conserved., 9 pages, 1 figure

The Hamiltonian mean-field (HMF) model describes particles on a ring interacting via a cosine interaction, or equivalently, rotors coupled by infinite-range XY interactions. Conceived as a generic statistical mechanical model for long-range interactions such as gravity (of which the cosine is the first Fourier component), it has recently been used to account for self-organization in experiments on cold atoms with long-range optically mediated interactions. The significance of the HMF model lies in its ability to capture the universal effects of long-range interactions and yet be exactly solvable in the canonical ensemble. In this work we consider the quantum version of the HMF model in one dimension and provide a classification of all possible stationary solutions of its generalized Gross-Pitaevskii equation (GGPE), which is both nonlinear and nonlocal. The exact solutions are Mathieu functions that obey a nonlinear relation between the wave function and the depth of the mean-field potential, and we identify them as bright solitons. Using a Galilean transformation these solutions can be boosted to finite velocity and are increasingly localized as the mean-field potential becomes deeper. In contrast to the usual local GPE, the HMF case features a tower of solitons, each with a different number of nodes. Our results suggest that long-range interactions support solitary waves in a novel manner relative to the short-range case.

Development of thermodynamic induction up to second order gives a dynamical bifurcation for thermodynamic variables and allows for the prediction and detailed explanation of nonequilibrium phase transitions with associated spontaneous symmetry breaking. By taking into account nonequilibrium fluctuations, long range order is analyzed for possible pattern formation. Consolidation of results up to second order produces thermodynamic potentials that are maximized by stationary states of the system of interest. These new potentials differ from the traditional thermodynamic potentials. In particular a generalized entropy is formulated for the system of interest which becomes the traditional entropy when thermodynamic equilibrium is restored. This generalized entropy is maximized by stationary states under nonequilibrium conditions where the standard entropy for the system of interest is not maximized. These new nonequilibrium concepts are incorporated into traditional thermodynamics, such as a revised thermodynamic identity, and a revised canonical distribution. Detailed analysis shows that the second law of thermodynamics is never violated even during any pattern formation, thus solving the entropic coupling problem. Examples discussed include pattern formation during phase front propagation under nonequilibrium conditions and the formation of Turing patterns. The predictions of second order thermodynamic induction are consistent with both observational data in the literature as well as the modeling of this data.

We consider the construction of a generalized Gibbs ensemble composed of complete bases of conserved charges in the repulsive Lieb-Liniger model. We will show that it is possible to construct these bases with varying locality as well as demonstrating that such constructions are always possible provided one has in hand at least one complete basis set of charges. This procedure enables the construction of bases of charges that possess well defined, finite expectation values given an arbitrary initial state. We demonstrate the use of these charges in the context of two different quantum quenches: a quench where the strength of the interactions in a one-dimensional gas is switched suddenly from zero to some finite value and the release of a one dimensional cold atomic gas from a confining parabolic trap. While we focus on the Lieb-Liniger model in this paper, the principle of the construction of these charges applies to all integrable models, both in continuum and lattice form., Comment: 18 pages, 7 figures

In systems with long-range interactions, since energy is a nonadditive quantity, ensemble inequivalence can arise: it is possible that different statistical ensembles lead to different equilibrium descriptions, even in the thermodynamic limit. The microcanonical ensemble should be considered the physically correct equilibrium distribution as long as the system is isolated. The canonical ensemble, on the other hand, can always be defined mathematically, but it is quite natural to wonder to which physical situations it does correspond. We show numerically and, in some cases, analytically that the equilibrium properties of a generalized Hamiltonian mean-field model in which ensemble inequivalence is present are correctly described by the canonical distribution in (at least) two different scenarios: (a) when the system is coupled via local interactions to a large reservoir (even if the reservoir shows, in turn, ensemble inequivalence), and (b) when the mean-field interaction between a small part of a system and the rest of it is weakened by some kind of screening.

An unusual correlation function was conjectured by Campostrini et al. [Phys. Rev. E 91, 042123 (2015)PLEEE81539-375510.1103/PhysRevE.91.042123] for the ground state of a transverse Ising chain with geometrical frustration. Later, we provided a rigorous proof for it and demonstrated its nonlocal nature based on an evaluation of a Toeplitz determinant in the thermodynamic limit [J. Stat. Mech. (2016) 11310210.1088/1742-5468/2016/11/113102]. In this paper, we further prove that all the low excited energy states forming the gapless kink phase share the same asymptotic correlation function with the ground state. As a consequence, the thermal correlation function almost remains constant at low temperatures if one assumes a canonical ensemble.

International audience; We study a one dimensional Coulomb system, where two charged colloids are neutralized by a collection of point counterions, with global neutrality. Temperature being given, two situations are addressed: the colloids are either kept at fixed positions (canonical ensemble), or the force acting on the colloids is fixed (isobaric-isothermal ensemble). The corresponding partition functions are worked out exactly, in view of determining which arrangement of counterions is optimal: how many counterions should be in the confined segment between the colloids? For the remaining ions outside, is there a left/right symmetry breakdown? We evidence a cascade of transitions, as system size is varied in the canonical treatment, or as pressure is increased in the isobaric formulation.

We perform microscopic molecular dynamics simulations of particle chains with an onsite anharmonicity to study relaxation of spatially homogeneous states to equilibrium, and directly compare the simulations with the corresponding Boltzmann-Peierls kinetic theory. The Wigner function serves as common interface between the microscopic and kinetic level. We demonstrate quantitative agreement after an initial transient time interval. In particular, besides energy conservation, we observe the additional quasi-conservation of the phonon density, defined via an ensemble average of the related microscopic field variables and exactly conserved by the kinetic equations. On super-kinetic time scales, density quasi-conservation is lost while energy remains conserved, and we find evidence for eventual relaxation of the density to its canonical ensemble value. However, the precise mechanism remains unknown and is not captured by the Boltzmann-Peierls equations., 9 pages, 11 figures

We propose a model molecule to investigate microscopic properties of a binary mixture with a closed-loop coexistence region. The molecule is comprised of a Lennard-Jones particle and a uniaxial quadrupole. Gibbs ensemble Monte Carlo simulations demonstrate that the high-density binary fluid of the molecules with the quadrupoles of the same magnitude but of the opposite signs can show closed-loop immiscibility. We find that an increase in the magnitude of the quadrupoles causes a shrinkage of the coexistence region. Molecular dynamics simulations also reveal that aggregates with two types of molecules arranged alternatively are formed in the stable one-phase region both above and below the coexistence region. String structures are dominant below the lower critical solution temperature, while branched aggregates are observed above the upper critical solution temperature. We conclude that the anisotropic interaction between the quadrupoles of the opposite signs plays a crucial role in controlling these properties of the phase behavior.

Grand-canonical fluctuations of Bose-Einstein condensates of light are accessible to state-of-the-art experiments [J. Schmitt et al., Phys. Rev. Lett. 112, 030401 (2014).]. We phenomenologically describe these fluctuations by using the grand-canonical ensemble for a weakly interacting Bose gas at thermal equilibrium. For a two-dimensional harmonic trap, we use two models for which the canonical partition functions of the weakly interacting Bose gas are given by exact recurrence relations. We find that the grand-canonical condensate fluctuations for weakly interacting Bose gases vanish at zero temperature, thus behaving qualitatively similar to an ideal gas in the canonical ensemble (or micro-canonical ensemble) rather than the grand-canonical ensemble. For low but finite temperatures, the fluctuations remain considerably higher than for the canonical ensemble, as predicted by the ideal gas in the grand-canonical ensemble, thus clearly showing that we are not in a regime in which the ensembles are equivalent., Comment: 13 pages, 7 figures, revised manuscript

We study in great detail the possible existence of a Renyi-associated thermodynamics, with negative results. In particular, we uncover a hidden relation in Renyi's variational problem (MaxEnt). This relation connects the two associated Lagrange multipliers (canonical ensemble) with the mean energy U and the Renyi parameter α. As a consequence of such relation, we obtain anomalous Renyi-MaxEnt thermodynamic results., Instituto de Física La Plata, Departamento de Física, Departamento de Matemáticas

We present a deterministic algorithm called contact density dynamics that generates any prescribed target distribution in the physical phase space. Akin to the famous model of Nosé and Hoover, our algorithm is based on a non-Hamiltonian system in an extended phase space. However, the equations of motion in our case follow from contact geometry and we show that in general they have a similar form to those of the so-called density dynamics algorithm. As a prototypical example, we apply our algorithm to produce a Gibbs canonical distribution for a one-dimensional harmonic oscillator.

Bose-Einstein condensation (BEC) of a noninteracting Bose gas of N particles in a two-dimensional box with Dirichlet boundary conditions is studied. Confirming previous work, we find that BEC occurs at finite N at low temperatures T without the occurrence of a phase transition. The conventionally-defined transition temperature TE for an infinite 3D system is shown to correspond in a 2D system with finite N to a crossover temperature between a slow and rapid increase in the fractional boson occupation N0/N of the ground state with decreasing T. We further show that TE ~ 1/log(N) at fixed area per boson, so in the thermodynamic limit there is no significant BEC in 2D at finite T. Thus, paradoxically, BEC only occurs in 2D at finite N with no phase transition associated with it. Calculations of thermodynamic properties versus T and area A are presented, including Helmholtz free energy, entropy S , pressure p, ratio of p to the energy density U/A, heat capacity at constant volume (area) CV and at constant pressure Cp, isothermal compressibility kappa_T and thermal expansion coefficient alpha_p, obtained using both the grand canonical ensemble (GCE) and canonical ensemble (CE) formalisms. The GCE formalism gives acceptable predictions for S, p, p/(U/A), kappa_T and alpha_p at large N, T and A, but fails for smaller values of these three parameters for which BEC becomes significant, whereas the CE formalism gives accurate results for all thermodynamic properties of finite systems even at low T and/or A where BEC occurs., Comment: 21 pages, 18 figures, 3 tables, 34 references

Stealthy potentials, a family of long-range isotropic pair potentials, produce infinitely degenerate disordered ground states at high densities and crystalline ground states at low densities in d-dimensional Euclidean space R^{d}. In the previous paper in this series, we numerically studied the entropically favored ground states in the canonical ensemble in the zero-temperature limit across the first three Euclidean space dimensions. In this paper, we investigate using both numerical and theoretical techniques metastable stacked-slider phases, which are part of the ground-state manifold of stealthy potentials at densities in which crystal ground states are favored entropically. Our numerical results enable us to devise analytical models of this phase in two, three, and higher dimensions. Utilizing this model, we estimated the size of the feasible region in configuration space of the stacked-slider phase, finding it to be smaller than that of crystal structures in the infinite-system-size limit, which is consistent with our recent previous work. In two dimensions, we also determine exact expressions for the pair correlation function and structure factor of the analytical model of stacked-slider phases and analyze the connectedness of the ground-state manifold of stealthy potentials in this density regime. We demonstrate that stacked-slider phases are distinguishable states of matter; they are nonperiodic, statistically anisotropic structures that possess long-range orientational order but have zero shear modulus. We outline some possible future avenues of research to elucidate our understanding of this unusual phase of matter.

We consider an exclusion process on a ring in which a particle hops to an empty neighbouring site with a rate that depends on the number of vacancies $n$ in front of it. In the steady state, using the well known mapping of this model to the zero range process, we write down an exact formula for the partition function and the particle-particle correlation function in the canonical ensemble. In the thermodynamic limit, we find a simple analytical expression for the generating function of the correlation function. This result is applied to the hop rate $u(n)=1+(b/n)$ for which a phase transition between high-density laminar phase and low-density jammed phase occurs for $b > 2$. For these rates, we find that at the critical density, the correlation function decays algebraically with a continuously varying exponent $b-2$. We also calculate the two-point correlation function above the critical density, and find that the correlation length diverges with a critical exponent $��=1/(b-2)$ for $b < 3$ and $1$ for $b > 3$. These results are compared with those obtained using an exact series expansion for finite systems., Accepted in Phys. Rev. E

The binodal of a boson square-well fluid is determined as a function of the particle mass through a quantum Gibbs ensemble Monte Carlo algorithm devised by R. Fantoni and S. Moroni [J. Chem. Phys. (to be published)]. In the infinite mass limit we recover the classical result. As the particle mass decreases, the gas-liquid critical point moves at lower temperatures. We explicitly study the case of a quantum delocalization de Boer parameter close to the one of (4)He. For comparison, we also determine the gas-liquid coexistence curve of (4)He for which we are able to observe the binodal anomaly below the λ-transition temperature.

The classical wave-particle Hamiltonian is considered in its generalized version, where two modes are assumed to interact with the co-evolving charged particles. The equilibrium statistical mechanics solution of the model is worked out analytically, both in the canonical and the microcanonical ensembles. The competition between the two modes is shown to yield ensemble inequivalence, at variance with the standard scenario where just one wave is allowed to develop. As a consequence, both temperature jumps and negative specific heat can show up in the microcanonical ensemble. The relevance of these findings for both plasma physics and Free Electron Laser applications is discussed., 5 pages, 2 figures

Based on the properties of exponential distribution families we analyze the Fisher information of the Gibbs canonical ensemble to construct a new state function for simple systems with no mechanical work. This function possesses nice symmetry properties with respect to Legendre transform and provides a connection with previous alternative formulations of thermodynamics, most notably the work by Biot, Serrin, and Frieden and collaborators. Logical extensions to systems with mechanical work may similarly consider generalized Gibbs ensembles.

Starting from the quantum description of isolated systems on the microscopic level we derive the two-generator formulation of nonequilibrium thermodynamics by means of the projection-operator technique. As a generalized canonical ensemble is employed, we obtain a convenient starting point for practical calculations in nonequilibrium thermodynamics; in particular, also in the classical limit. All dynamical material properties are contained in a canonical nonequilibrium correlation. However, the generalized canonical approach is inappropriate for systems with large fluctuations; possible steps toward a suitable generalization for quantum systems are discussed.

In this article we show that the inhomogeneous density obtained from a density-functional theory of classical fluids in the canonical ensemble (CE), recently presented by White et al [Phys. Rev. Lett. 84 (2000) 1220], is equivalent to first order to the result of the series expansion of the CE inhomogeneous density introduced by Gonzalez et al [Phys. Rev. Lett. 79 (1997) 2466]., Comment: 6 pages, RevTeX

We study a model of unsupervised learning where the real-valued data vectors are isotropically distributed, except for a single symmetry breaking binary direction $\bm{B}\in\{-1,+1\}^{N}$, onto which the projections have a Gaussian distribution. We show that a candidate vector $\bm{J}$ undergoing Gibbs learning in this discrete space, approaches the perfect match $\bm{J}=\bm{B}$ exponentially. Besides the second order ``retarded learning'' phase transition for unbiased distributions, we show that first order transitions can also occur. Extending the known result that the center of mass of the Gibbs ensemble has Bayes-optimal performance, we show that taking the sign of the components of this vector leads to the vector with optimal performance in the binary space. These upper bounds are shown not to be saturated with the technique of transforming the components of a special continuous vector, except in asymptotic limits and in a special linear case. Simulations are presented which are in excellent agreement with the theoretical results., Comment: 18 pages, 11 EPS figures; submitted

We investigate to what extend the replica-exchange Monte Carlo method is able to equilibrate a simple liquid in its supercooled state. We find that this method does indeed allow to generate accurately the canonical distribution function even at low temperatures and that its efficiency is about 10-100 times higher than the usual canonical molecular dynamics simulation., 6 pages, 5 figures

To properly model highly entropic inhomogeneous materials in the canonical ensemble by molecular dynamics simulations, it is necessary to choose algorithms which rigorously implement the ensemble. Approximate methods may have either very low efficiency or completely fail in the very soft regime. The calculation of the shear modulus of the diluted central force network is used to illustrate this point. Four algorithms to realize the canonical ensemble have been tested on two methods of evaluation of the shear modulus.

Fluctuations of the instantaneous local Lagrangian strain $\epsilon_{ij}(\bf{r},t)$, measured with respect to a static ``reference'' lattice, are used to obtain accurate estimates of the elastic constants of model solids from atomistic computer simulations. The measured strains are systematically coarse- grained by averaging them within subsystems (of size $L_b$) of a system (of total size $L$) in the canonical ensemble. Using a simple finite size scaling theory we predict the behaviour of the fluctuations $$ as a function of $L_b/L$ and extract elastic constants of the system {\em in the thermodynamic limit} at nonzero temperature. Our method is simple to implement, efficient and general enough to be able to handle a wide class of model systems including those with singular potentials without any essential modification. We illustrate the technique by computing isothermal elastic constants of the ``soft'' and the hard disk triangular solids in two dimensions from molecular dynamics and Monte Carlo simulations. We compare our results with those from earlier simulations and density functional theory., Comment: 24 pages REVTEX, 10 .ps figures, version accepted for publication in Physical Review E

A system of N classical particles in a two-dimensional periodic cell interacting via a long-range attractive potential is studied numerically and theoretically. For low energy density U a collapsed phase is identified, while in the high energy limit the particles are homogeneously distributed. A phase transition from the collapsed to the homogeneous state occurs at critical energy Uc . A theoretical analysis within the canonical ensemble identifies such a transition as first order. But microcanonical simulations reveal a negative specific heat regime near Uc . This suggests that the transition belongs to the universality class previously identified by Hertel and Thirring @Ann. Phys. ~N.Y.! 63, 520 ~1970!# for gravitational lattice gas models. The dynamical behavior of the system is strongly affected by this transition: below Uc anomalous diffusion is observed, while for U.Uc the motion of the particles is almost ballistic. In the collapsed phase, finite N effects act like a ‘‘deterministic’’ noise source of variance O(1/N), that restores normal diffusion on a time scale that diverges with N. As a consequence, the asymptotic diffusion coefficient will also diverge algebraically with N and superdiffusion will be observable at any time in the limit N!‘. A Lyapunov analysis reveals that for U .Uc the maximal exponent l decreases proportionally to N 21/3 and vanishes in the mean-field limit. For sufficiently small energy, in spite of a clear nonergodicity of the system, a common scaling law l}U 1/2 is observed for various different initial conditions. In the intermediate energy range, where anomalous diffusion is observed, a strong intermittency is found. This intermittent behavior is related to two different dynamical mechanisms of chaotization. @S1063-651X~99!10303-9#

Fluids of dipolar hard spheres are thought to have rather unusual phase behavior in that liquid-vapor equilibrium has not been observed in computer simulations. Recently, McGrother and Jackson [Phys. Rev. Lett. 76, 4183 (1996)] have reported Gibbs ensemble Monte Carlo (GEMC) results for dipolar hard spherocylinders. At the reduced temperature ${T}^{*}=0.12$ they report liquid-vapor coexistence for aspect ratios $L/D\ensuremath{\gtrsim}0.19,$ but no coexistence was found for smaller values. In the present paper we investigate the phase behavior of dipolar hard dumbbells and dipolar hard spherocylinders using both GEMC and grand canonical Monte Carlo methods. For both models at the same reduced temperature we find liquid-vapor coexistence for aspect ratios as low as 0.1. For aspect ratios $\ensuremath{\lesssim}0.1,$ the strong dipolar interactions create severe sampling problems and reliable results cannot be obtained. This is particularly true for the GEMC method and possibly accounts for the disagreement we find with the earlier simulations.

We show the existence of a fluid-fluid demixing transition in binary mixtures of nonadditive asymmetric hard-sphere mixtures by performing Gibbs ensemble Monte Carlo simulations for a size ratio of 0.1 and varying degrees of nonadditivity. We compare our results with the theoretical binodals obtained from the equation of state proposed by Barboy and Gelbart [J. Chem. Phys. 71, 3053 (1979)] and we find reasonable agreement for sufficiently large values of the nonadditivity parameter. Upon decreasing the nonadditivity parameter, we find that the fluid-fluid demixing region shifts to higher pressures and becomes narrower. For sufficiently small nonadditivities, we do not find a fluid-fluid demixing transition for total packing fractions $l0.5.$

We present results from a molecular dynamics simulation of an unconfined Gay-Berne film in equilibrium with its own saturated vapor. The parametrization and temperature range used are based upon the results of preliminary Gibbs ensemble investigations, which show the existence of bulk liquid-vapor and nematic-vapor coexistence. This parametrization is found to induce a preferred molecular alignment in the nematic film perpendicular to the liquid-vapor interface, in contrast to work on similar systems showing planar alignment. At slightly higher temperatures the nematic phase is wet by the isotropic, displaying an intermediate ordering regime in which the film is comprised of several short-lived nematic domains. This behavior has been analyzed using orientational correlation functions, and shown to be associated with a decoupling of the planar and perpendicular nematic ordering. The interfacial surface tension behavior has also been evaluated, and shown to be consistent with theoretical predictions for systems displaying isotropic wetting.

We have recently shown that the low-temperature velocity power spectrum of an anharmonic oscillator (AHO) in a canonical ensemble is recovered when one considers the AHO as coupled via harmonic springs to a system of noninteracting harmonic oscillators (HO's), each with the same characteristic frequency as that of the AHO [D.P. Visco, Jr. and S. Sen, Phys. Rev. E 57, 224 (1998)]. In the present work, we generalize our earlier study by establishing the following points. (i) We show that when the AHO is coupled via anharmonic springs to a system of noninteracting HO's, each with characteristic frequency as that of the AHO, the dynamics of the AHO is strongly affected by the altered coupling and hence we contend that the bath particles must be connected via harmonic springs to preserve the dynamics of the AHO. (ii) We consider an AHO with a characteristic frequency that differs from that of the bath particles and show that the correct dynamics of the new AHO is recovered when (a) the harmonic oscillators that make up the bath particles have constrained movement and (b) the bath particles are harmonically coupled at significantly weakened strength compared to the study in case (i) above.

The vapor-liquid equilibria of a monomer-dimer square-well mixture is examined. The square-well segments all have equal diameter, well depth, and range $(\ensuremath{\lambda}=1.5);$ the dimers are formed from two tangentially bonded monomers. The phase behavior in this system is thus governed by the difference in molecular length of the two components. Pressure-composition slices of the phase diagram are obtained from Gibbs ensemble simulation of the mixture for a wide range of temperatures, including both subcritical and supercritical states. A small negative deviation from ideality is observed. The simulation data are used to determine the vapor-liquid critical line of the mixture. Additionally, we extrapolate the mixture data to obtain an estimate of the pure component phase equilibria. The resulting values for the coexistence envelope are in good agreement with existing data, and new vapor pressures of the square-well dimer are reported. The vapor-liquid equilibria data are used to establish the adequacy of the statistical associating fluid theory for potentials of variable range. The theory is found to give an excellent representation of the phase behavior of both the pure components and of the mixture.

In the last few years generalized ensemble algorithms have become popular as a way to overcome the exponentially slow convergence in numerical simulations of systems with a rough energy landscape. Prominent examples of such an approach are the multicanonical algorithm @1,2#, 1/k sampling @3#, and simulated tempering @4,5#. These algorithms explore larger parts of the phase space than canonical molecular dynamics or Monte Carlo, which at low temperatures are easily trapped in one of the huge number of local minimas. This is because in the canonical ensemble the probability to cross an energy barrier of heights DE is proportional to e at temperature T . On the other hand, in generalized ensembles the probability to cross an energy barrier is independent of temperature. For instance, in the multicanonical algorithm @1,2#, configurations with energy E are updated with a weight