Search

At thermal equilibrium, intensive quantities like temperature and pressure have to be uniform throughout the system, restricting inhomogeneous systems composed of different phases. The paradigmatic example is the coexistence of vapor and liquid, a state that can also be observed for active Brownian particles steadily driven away from equilibrium. Recently, a strategy has been proposed that allows to predict phase equilibria of active particles [Solon et al., Phys. Rev. E 97, 020602(R) (2018)2470-004510.1103/PhysRevE.97.020602]. Here we elaborate on this strategy and formulate it in the framework of a van der Waals theory for active disks. For a given equation of state, we derive the effective free energy analytically and show that it yields coexisting densities in very good agreement with numerical results. We discuss the interfacial tension and the relation to Cahn-Hilliard models.

Microorganisms such as bacteria are active matters which consume chemical energy and generate their unique run-and-tumble motion. A swarm of such microorganisms provide a nonequilibrium active environment whose noise characteristics are different from those of thermal equilibrium reservoirs. One important difference is a finite persistence time, which is considerably large compared to that of the equilibrium noise, that is, the active noise is colored. Here, we study a mesoscopic energy-harvesting device (engine) with active reservoirs harnessing this noise nature. For a simple linear model, we analytically show that the engine efficiency can surpass the conventional Carnot bound, thus the power-efficiency tradeoff constraint is released, and the efficiency at the maximum power can overcome the Curzon-Ahlborn efficiency. We find that the supremacy of the active engine critically depends on the time-scale symmetry of two active reservoirs., Comment: Supplemental Material included

An explicit expression for the temperature of an open two-level quantum system is obtained as a function of local properties, under the hypothesis of weak interaction with the environment. This temperature is defined for both equilibrium and out-of-equilibrium states, and coincides with the environment temperature if the system reaches thermal equilibrium with a heat reservoir. Additionally, we show that within this theoretical framework the total entropy production can be partitioned into two contributions: one due to heat transfer, and another, associated to internal irreversibilities, related to the loss of internal coherence by the qubit. The positiveness of the heat capacity is established, as well as its consistency with the well known results at thermal equilibrium. We apply these concepts to two different systems, and show that they behave in analogous ways as their classical counterparts.

The celebrated Sutherland-Einstein relation for systems at thermal equilibrium states that spread of trajectories of Brownian particles is an increasing function of temperature. Here, we scrutinize the diffusion of underdamped Brownian motion in a biased periodic potential and analyze regimes in which a diffusion coefficient decreases with increasing temperature within a finite temperature window. Comprehensive numerical simulations of the corresponding Langevin equation performed with unprecedented resolution allow us to construct a phase diagram for the occurrence of the nonmonotonic temperature dependence of the diffusion coefficient. We discuss the relation of the later effect with the phenomenon of giant diffusion.

In this paper, we show how plasma discharge capillaries can be numerically modeled as resistors within an RLC-series discharge circuit, allowing for a simple description of these systems, while taking into account heat and radiation losses. An analytic radial model is also provided and compared to the numerical model for plasma discharge capillaries at thermal equilibrium, with corrections due to radiation losses. Finally, diagnostic techniques based on visible spectroscopy of plasma emission lines are discussed both for atomic and molecular gases, comparing experimental results with numerical simulations and theoretical calculations.

In the context of an ultracold Fermi gas, we derive conservation laws for mass, energy and momentum based on a generalized nonlocal Boltzmann equation with gradient corrections in the collision integral. The corrections are expressed in terms of effective collision duration, particle displacement and changes of total momentum and energy. Their origin is in the in-medium $T$ matrix. Using variations of the optical theorem, we show that in the collision integral the particle-hole symmetry can be recast into a form of collision symmetry amenable to semiclassical simulation. Pauli-blocked collisions are distinguished from Bose-stimulated nondissipative ones; the latter are not present in the absence of gradient corrections. Consolidating with the microscopic theory, we extract local conservation laws for a general time-dependent interaction potential, and demonstrate how both types of collisions affect densities and flows of conserving quantities. Comparison is made with the approach of Nozi\`eres and Schmitt-Rink in the limit of thermal equilibrium. Under approximations used for normal-state ultracold Fermi gases interacting via Feshbach resonances we demonstrate the effect of the collision delay on the shear viscosity.

The canonical probability distribution describes a system in thermal equilibrium with an infinite heat bath. When the bath is finite the distribution is modified. These modifications can be derived by truncating a Taylor-series expansion of the entropy of the heat bath, but their form depends on the expansion parameter chosen. We consider two such expansions, which yield supercanonical (i.e., higher-order canonical) distributions of exponential and power-law form. The latter is identical in form to the ``Tsallis distribution,'' which is therefore a valid asymptotic approximation for an arbitrary finite heat bath, but bears no intrinsic relation to Tsallis entropy.

A numerical study is presented of a free particle interacting with a deterministic thermostat in which the usual friction force is supplemented with a fluctuating force that depends on the self-consistent damping coefficient associated with coupling to the heat bath. It is found that this addition results in a chaotic environment in which a particle self-heats from rest and moves in positive and negative directions, exhibiting a characteristic diffusive behavior. The frequency power spectrum of the dynamical quantities displays the exponential frequency dependence ubiquitous to chaotic dynamics. The velocity distribution function approximates a Maxwellian distribution, but it does show departures from perfect thermal equilibrium, while the distribution function for the damping coefficient shows a closer fit. The behavior for the classic Nosé-Hoover (NH) thermostat is compared to that of the enlarged Martyna-Klein-Tuckerman (MKT) model. Over a narrow amplitude range, the application of a constant external force results quantitatively in the Einstein relation for the NH thermostat, and for the MKT model it differs by a factor of 2.

The second law of thermodynamics governs the direction of heat transport, which provides the foundational definition of thermodynamic Clausius entropy. The definitions of entropy are further generalized for the phenomenological heat transport models in the frameworks of classical irreversible thermodynamics and extended irreversible thermodynamics (EIT). In this work, entropic functions from mathematics are combined with phenomenological heat conduction models and connected to several information-geometrical conceptions. The long-time behaviors of these mathematical entropies exhibit a wide diversity and physical pictures in phenomenological heat conductions, including the tendency to thermal equilibrium, and exponential decay of nonequilibrium and asymptotics, which build a bridge between the macroscopic and microscopic modelings. In contrast with the EIT entropies, the mathematical entropies expressed in terms of the internal energy function can avoid singularity paired with nonpositive local absolute temperature caused by non-Fourier heat conduction models.

The linear response is investigated in a long-range Hamiltonian system from the view point of dynamics, which is described by the Vlasov equation in the limit of large population. Due to existence of the Casimir invariants of the Vlasov dynamics, an external field does not drive the system to the forced thermal equilibrium in general, and the linear response is suppressed. With the aid of a linear response theory based on the Vlasov dynamics, we compute the suppressed linear response in a system having two order parameters, which introduce the conjugate two external fields and the susceptibility matrix of size two accordingly. Moreover, the two order parameters bring three phases and the three types of second-order phase transitions between two of them. For each type of the phase transitions, all the critical exponents for elements of the susceptibility matrix are computed. The critical exponents reveal that some elements of the matrices do not diverge even at critical points, while the mean-field theory predicts divergences. The linear response theory also suggests appearance of negative off-diagonal elements, in other words, an applied external field decreases the value of an order parameter. These theoretical predictions are confirmed by direct numerical simulations of the Vlasov equation., Comment: 14 pages, 6 figures

We study the thermal transport properties of the one dimensional Fermi-Pasta-Ulam model ($\beta$-type) with long-range interactions. The strength of the long-range interaction decreases with the (shortest) distance between the lattice sites as ${distance}^{-\delta}$, where $\delta \ge 0$.Two Langevin heat baths at unequal temperatures are connected to the ends of the one dimensional lattice via short-range harmonic interactions that drive the system away from thermal equilibrium. In the nonequilibrium steady state the heat current, thermal conductivity and temperature profiles are computed by solving the equations of motion numerically. It is found that the conductivity $\kappa$ has an interesting non-monotonic dependence with $\delta$ with a maximum at $\delta = 2.0$ for this model. Moreover, at $\delta = 2.0$, $\kappa$ diverges almost linearly with system size $N$ and the temperature profile has a negligible slope, as one expects in ballistic transport for an integrable system. We demonstrate that the non-monotonic behavior of the conductivity and the nearly ballistic thermal transport at $\delta = 2.0$ obtained under nonequilibrium conditions can be explained consistently by studying the variation of largest Lyapunov exponent $\lambda_{max}$ with $\delta$, and excess energy diffusion in the equilibrium microcanonical system., Comment: 8 pages, 9 figures

We show that the Bayesian inference of recently measured x-ray diffraction spectra from laser-shocked aluminum [L. B. Fletcher et al., Nat. Photon. 9, 274 (2015)10.1038/nphoton.2015.41] with the one-component-plasma (OCP) model performs remarkably well at estimating the ionic density and temperature. This statistical approach requires many evaluations of the OCP static structure factor, which were done using a recently derived analytic fit. The atomic form factor is approximated by an exponential function in the diffraction window of the first peak. The electronic temperature is then estimated from a comparison of this approximated form factor with the electronic structure of an average atom model. Out-of-equilibrium states, with electrons hotter than ions, are diagnosed for the spectra obtained early after the pump, whereas at a late time delay the plasma is at thermal equilibrium. Apart from the present findings, this OCP-based modeling of warm dense matter has an important role to play in the interpretation of x-ray Thomson scattering measurements currently performed at large laser facilities.

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 quantify the disorder-induced heating (DIH) of ultracold neutral plasmas (UCNPs) created from cold atoms in optical lattices with partial filling fractions, using a conservation of energy model involving the spatial correlations of the initial state and the equation of state in thermal equilibrium for a one-component plasma. We show, for experimentally achievable filling fractions, that the ionic Coulomb coupling parameter could be increased to a degree comparable to other proposed DIH-mitigation schemes. Molecular dynamics simulations were performed with compensation for finite-size and periodic boundary effects, which agree with calculations using the model. Reduction of DIH using optical lattices will allow for the study of strongly coupled plasma physics using low-density, low-temperature, laboratory-based plasmas, and lead to improved brightness in UCNP-based cold electron and ion beams, where DIH is otherwise a fundamental limitation to beam focal sizes and diffraction imaging capability.

We numerically exhibit two strange phenomena of finite-size fluctuation in thermal equilibrium of a paradigmatic long-range interacting system having a second-order phase transition. One is a nonclassical finite-size scaling at the critical point, which differs from the prediction by statistical mechanics. With the aid of this strange scaling, the scaling theory for infinite-range models conjectures the nonclassical values of critical exponents for the correlation length. The other is relaxation of the fluctuation strength from one level to another in spite of being in thermal equilibrium. A scenario is proposed to explain these phenomena from the viewpoint of the Casimir invariants and their nonexactness in finite-size systems, where the Casimir invariants are conserved in the Vlasov dynamics describing the long-range interacting systems in the limit of large population. This scenario suggests appearance of the reported phenomena in a wide class of isolated long-range interacting systems.

Demonstrating how microscopic dynamics cause large systems to approach thermal equilibrium remains an elusive, longstanding, and actively-pursued goal of statistical mechanics. We identify here a dynamical mechanism for thermalization in a general class of two-component dynamical Lorentz gases, and prove that each component, even when maintained in a non-equilibrium state itself, can drive the other to a thermal state with a well-defined effective temperature., 5 pages, 5 figures

We first study fluctuating hydrodynamics (FH) at equilibrium in periodic domains by use of the smoothed dissipative particle dynamics (SDPD) method. We examine the performance of SDPD by comparing it with the theory of FH. We find that the spatial correlation of particle velocity is always the Dirac δ function, irrespective of numerical resolution, in agreement with the theory. However, the spatial correlation of particle density has a finite range of r(c), which is due to the kernel smoothing procedure for the density. Nevertheless, this finite range of correlation can be reduced to an arbitrarily small value by increasing the resolution, that is, reducing r(c), similarly to how the smoothing kernel converges to the Dirac δ function. Moreover, we consider temporal correlation functions (CFs) of random field variables in Fourier space. For sufficient resolution, the CFs of SDPD simulations agree very well with analytical solutions of the linearized FH equations. This confirms that both the shear and sound modes are modeled accurately and that fluctuations are generated, transported, and dissipated in both thermodynamically and hydrodynamically consistent ways in SDPD. We also show that the CFs of the classical dissipative particle dynamics (DPD) method with proper parameters can recover very well the linearized solutions. As a reverse implication, the measurement of CFs provides an effective means of extracting viscosities and sound speed of a DPD system with a new set of input parameters. Subsequently, we study the FH in truncated domains in the context of multiscale coupling via the domain decomposition method, where a SDPD simulation in one subdomain is coupled with a Navier-Stokes (NS) solver in an adjacent subdomain with an overlapping region. At equilibrium, the mean values of the NS solution are known a priori and do not need to be extracted from actual simulations. To this end, we model a buffer region as an equilibrium boundary condition (EBC) at the truncated side of the SDPD simulation. In the EBC buffer, the velocity of particles is drawn from a known Gaussian distribution, that is, the Maxwell-Boltzmann distribution. Due to the finite range of spatial correlation, the density of particles in the EBC buffer must be drawn from a conditional Gaussian distribution, which takes into account the available density distribution of neighboring interior particles. We introduce a Kriging method to provide such a conditional distribution and hence preserve the spatial correlation of density. Spatial and temporal correlations of SDPD simulations in the truncated domain are compared to that in a single complete domain. We find that a gap region between the buffer and interior is important to reduce the extra dissipation generated by the artificial buffer at equilibrium, rendering more investigations necessary for thermal fluctuations in the multiscale coupling of nonequilibrium flows.

We investigate response to an external magnetic field in the Hamiltonian mean-field model, which is a paradigmatic toy model of a ferromagnetic body and consists of plane rotators like the XY spins. Due to long-range interactions, the external field drives the system to a long-lasting quasistationary state before reaching thermal equilibrium, and the susceptibility tensor obtained in the quasista- tionary state is predicted by a linear response theory based on the Vlasov equation. For spatially homogeneous stable states, whose momentum distributions are asymmetric with zero-means, the theory reveals that the susceptibility tensor for an asymptotically constant external field is neither symmetric nor diagonalizable, and the predicted states are not stationary accordingly. Moreover, the tensor has no divergence even at the stability threshold. These theoretical findings are confirmed by direct numerical simulations of the Vlasov equation for the skew-normal distribution functions., 10 pages, 8 figures

We ask what happens when two nonequilibrium systems in steady state are kept in contact and allowed to exchange a quantity, say mass, which is conserved in the combined system. Will the systems eventually evolve to a new stationary state where a certain intensive thermodynamic variable, like equilibrium chemical potential, equalizes following the zeroth law of thermodynamics and, if so, under what conditions is it possible? We argue that an equilibriumlike thermodynamic structure can be extended to nonequilibrium steady states having short-ranged spatial correlations, provided that the systems interact weakly to exchange mass with rates satisfying a balance condition-reminiscent of a detailed balance condition in equilibrium. The short-ranged correlations would lead to subsystem factorization on a coarse-grained level and the balance condition ensures both equalization of an intensive thermodynamic variable as well as ensemble equivalence, which are crucial for construction of a well-defined nonequilibrium thermodynamics. This proposition is proved and demonstrated in various conserved-mass transport processes having nonzero spatial correlations.

We explore fluctuation relations in a periodically driven micromechanical torsional oscillator. In the linear regime where the modulation is weak, we verify that the ratio of the work variance to the mean work is constant, consistent with conventional fluctuation theorems. We then increase the amplitude of the periodic drive so that the response becomes nonlinear and two nonequilibrium oscillation states coexist. Due to interstate transitions, the work variance exhibits a peak at the driving frequency at which the occupation of the two states is equal. Moreover, the work fluctuations depend exponentially on the inverse noise intensity. Our data are consistent with recent theories on systems driven into bistability that predict generic behaviors different from conventional fluctuation theorems., To appear in Phys.Rev.E

An effective temperature $\ensuremath{\theta}$, conjugated to a generalized entropy ${s}_{q}$, was introduced recently for a system of interacting particles. Since $\ensuremath{\theta}$ presents values much higher than those of typical room temperatures $T\ensuremath{\ll}\ensuremath{\theta}$, the thermal noise can be neglected ($T/\ensuremath{\theta}\ensuremath{\simeq}0$) in these systems. Moreover, the consistency of this definition, as well as of a form analogous to the first law of thermodynamics, $du=\ensuremath{\theta}d{s}_{q}+\ensuremath{\delta}W$, were verified lately by means of a Carnot cycle, whose efficiency was shown to present the usual form, $\ensuremath{\eta}=1\ensuremath{-}({\ensuremath{\theta}}_{2}/{\ensuremath{\theta}}_{1})$. Herein we explore further the heat contribution $\ensuremath{\delta}Q=\ensuremath{\theta}d{s}_{q}$ by proposing a way for a heat exchange between two such systems, as well as its associated thermal equilibrium. As a consequence, the zeroth principle is also established. Moreover, we consolidate the first-law proposal by following the usual procedure for obtaining different potentials, i.e., applying Legendre transformations for distinct pairs of independent variables. From these potentials we derive the equation of state, Maxwell relations, and define response functions. All results presented are shown to be consistent with those of standard thermodynamics for $Tg0$.

A pure-dephasing reservoir acting on an individual quantum system induces loss of coherence without energy exchange. When acting on composite quantum systems, dephasing reservoirs can lead to a radically different behavior. Transport of energy between two pure-dephasing markovian reservoirs is predicted in this work. They are connected through a chain of coupled sites. The baths are kept in thermal equilibrium at distinct temperatures. Quantum coherence between sites is generated in the steady-state regime and results in the underlying mechanism sustaining the effect. A quantum model for the reservoirs is a necessary condition for the existence of stationary energy transport. A microscopic derivation of the non-unitary system-bath interaction is employed, valid in the ultrastrong inter-site coupling regime. The model assumes that each site-reservoir coupling is local., 8 pages, 2 figures

Subdiffusion in the presence or absence of an external force field is established on the basis of an extension of conventional Langevin dynamics to include long-tailed trapping events. It is demonstrated how the presence of the trapping events leads to the macroscopic observation of fractional diffusion, described by a fractional Klein-Kramers equation.

The relation between relaxation, the time scale of Lyapunov instabilities, and the Kolmogorov-Sinai time in a one-dimensional gravitating sheet system is studied. Both the maximum Lyapunov exponent and the Kolmogorov-Sinai entropy decrease as proportional to ${N}^{\ensuremath{-}1/5}.$ The time scales determined by these quantities evidently differ from any type of relaxation time found in the previous investigations. The relaxation time to quasiequilibria (microscopic relaxation) is found to have the same N dependence as the inverse of the minimum positive Lyapunov exponent. The relaxation time to the final thermal equilibrium differs from the inverse of the Lyapunov exponents and the Kolmogorov-Sinai time.

We introduce a model consisting of nonaligned and impenetrable particles. This model is obtained by placing particles of random orientation within "security spheres," typically chosen to be spheres in thermal equilibrium. The particles in general are allowed to be nonspherical. We obtain an analytical expression for the function S(n), the probability that n points simultaneously lie outside of the particle phase. This characterization of the microstructure appears in certain rigorous bounds on the effective properties of random materials. We also evaluate S2 for various specific examples of this model, including nonaligned impenetrable ellipsoids.

The propagation of a pulse in a nonlinear array of oscillators is influenced by the nature of the array and by its coupling to a thermal environment. For example, in some arrays a pulse can be speeded up while in others a pulse can be slowed down by raising the temperature. We begin by showing that an energy pulse (one dimension) or energy front (two dimensions) travels more rapidly and remains more localized over greater distances in an isolated array (microcanonical) of hard springs than in a harmonic array or in a soft-springed array. Increasing the pulse amplitude causes it to speed up in a hard chain, leaves the pulse speed unchanged in a harmonic system, and slows down the pulse in a soft chain. Connection of each site to a thermal environment (canonical) affects these results very differently in each type of array. In a hard chain the dissipative forces slow down the pulse while raising the temperature speeds it up. In a soft chain the opposite occurs: the dissipative forces actually speed up the pulse, while raising the temperature slows it down. In a harmonic chain neither dissipation nor temperature changes affect the pulse speed. These and other results are explained on the basis of the frequency vs energy relations in the various arrays.

We investigated the phase behavior near the order-disorder transition (ODT) temperature in a nearly symmetric diblock copolymer, using ultra-small-angle x-ray scattering method. In a narrow temperature range very close to the ODT temperature, we observed the scattering profiles that can be interpreted as a linear combination of the scattering from the disordered state and that from the ordered lamellar state. These profiles were stable during the observation time (50 h), revealing that the two-phase coexistence occurs at thermal equilibrium within this temperature range.

Onset in thermoacoustic engines, the transition to spontaneous self-generation of oscillations, is studied here as both a dynamical critical transition and a limiting heat engine behavior. The critical transition is interesting because it occurs for both dissipative and conservative systems, with common scaling properties. When conservative, the stable oscillations above the critical point also implement a reversible engine cycle satisfying Carnot{close_quote}s theorem, a universal conservation law for entropy flux. While criticality in equilibrium systems is naturally associated with symmetries and universal conservation laws, these are usually exploited with global minimization principles, which dynamical critical systems may not have if dissipation is essential to their criticality. Acoustic heat engines furnish an example connecting equilibrium methods with dynamical and possibly even dissipative critical transitions: A reversible engine is shown to map, by a change of variables, to an equivalent system in apparent thermal equilibrium; a Noether symmetry in the equilibrium field theory implies Carnot{close_quote}s theorem for the engine. Under the same association, onset is shown to be a process of spontaneous symmetry breaking and the scaling of the quality factor predicted for both the reversible {ital and irreversible} engines is shown to arise from the Ginzburg-Landau description of the broken phase. {copyright}more » {ital 1998} {ital The American Physical Society}« less

We have separately attached the two complementary strands of one end of a DNA double helix to a glass slide and a glass microneedle. Displacing the slide away from the needle, the molecule is progressively pulled open and the changing deflection of the needle gives the corresponding variation in the opening force. Force signals which are very rich in detail are reproducibly obtained. The average level and amplitude of the force signal is almost independent of the opening velocity in the interval 20 nm/s to 800 nm/s. A theoretical description based on the assumption of thermal equilibrium allows us to link the measured force curves to the genomic sequence of the DNA. A molecular stick-slip motion is revealed, which in contrast to the dynamics of macroscopic solid friction is a deterministic and reproducible process. This process is considered experimentally and theoretically. @S1063-651X~98!13208-7#

Superconducting magnet fringe field NMR diffusometry is applied to an adsorbate‐molecular sieve system in order to obtain intracrystalline self-diffusion of adsorbed molecules. Effects of self-diffusion, exchange, relaxation, and dipolar correlation are discussed. The proper equations for one- and two-dimensional anomalous self-diffusion with and without macroscopic order are derived. The method is applied to investigate methane self-diffusion in the molecular sieve silicoaluminophosphate, type 11 ~SAPO-11!. It is concluded that the nature of the methane displacements in the sieve channels is single-file self-diffusion. @S1063-651X~98!03906-3# PACS number~s!: 47.55.Mh, 66.30.2h, 76.60.2k, 81.05.Rm I. INTRODUCTION Molecular sieves are microporous materials, which possess a huge internal volume capable of adsorbing molecules of proper size. There is a large variety of intracrystalline structures restricting adsorbate displacements so that anomalous self-diffusion processes can be expected. Usually one investigates adsorbate diffusion in thermal equilibrium. In terms of a model with two states, ‘‘adsorbed’’ and ‘‘free,’’

We have performed nonequilibrium classical and quantum-mechanical molecular dynamics simulations that follow the interpenetration of deuterium-tritium (DT) and carbon (C) components through an interface initially in hydrostatic and thermal equilibrium. We concentrate on the warm, dense matter regime with initial densities of 2.5--5.5 g/cm${}^{3}$ and temperatures from 10 to 100 eV. The classical treatment employs a Yukawa pair-potential with the parameters adjusted to the plasma conditions, and the quantum treatment rests on an orbital-free density functional theory at the Thomas-Fermi-Dirac level. For times greater than about a picosecond, the component concentrations evolve in accordance with Fick's law for a classically diffusing fluid with the motion, though, described by the mutual diffusion coefficient of the mixed system rather than the self-diffusion of the individual components. For shorter times, microscopic processes control the clearly non-Fickian dynamics and require a detailed representation of the electron probability density in space and time.

The equilibrium statistical mechanics of one-dimensional lattice gases with interactions of arbitrary range and shape between first-neighbor atoms is solved exactly on the basis of statistically interacting vacancy particles. Two sets of vacancy particles are considered. In one set all vacancies are of one-cell size. In the other set the sizes of vacancy particles match the separation between atoms. Explicit expressions are obtained for the Gibbs free energy and the distribution of spaces between atoms at thermal equilibrium. Applications to various types of interaction potentials are discussed, including long-range potentials that give rise to phase transitions. Extensions to hard rod systems are straightforward and are shown to agree with existing results for lattice models and their continuum limits., Comment: 10 pages, 5 figures

We obtain conditions of phase equilibrium of a substance in a nonuniform potential field of forces. If the force per mass unit is phase dependent, the field may induce a shift of phase equilibrium. In this case, chemical potentials of the substance do not coincide at the phase boundary with equal temperatures and pressures for each phase. The equality condition at the phase boundary in the presence of the field for the full chemical potentials of the phases, including the additional field component, can be reduced to the equality condition of the chemical potentials under different pressures for each phase. Thus the field-induced phase equilibrium becomes impossible for a given geometry, and the system has to change its phase abruptly when one of the phases reaches its spinodal state. An example of such a transition is the case of a liquid current-carrying conductor in its own magnetic field rapidly turning to a dispersion state (drops in vapor). Similar phenomena can occur at the final stage of electrical explosion of conductors. We also show that for a liquid dielectric in a nonuniform external electric field the thermodynamical equilibrium state is liquid with vapor bubbles, the latter being localized into the domain of the higher value of the field.

Starting out with the thermodynamic balance equations of liquid crystalline films and the second law of thermodynamics, an analog to the global surface free energy is derived whose time derivative is negative definite out of equilibrium and zero in equilibrium. This evolution criterion allows one to formulate a variational principle for the equilibrium states by minimizing the modified global surface free energy derived above. Thus the quantity which is extremal in equilibrium in the case of free-standing crystalline films is not presupposed ad hoc, but derived from an evolution criterion based on the second law.

We obtain the low-temperature phases and phase transitions of the coadsorption of two monomer species on a semi-infinite square lattice of odd width M, with first- and second-neighbor interactions. We study the cases for which first-neighbor interactions between two monomers of the same species are repulsive, allowing all other interactions to be attractive or repulsive. Most of the numerical results are found to fit exact closed-form expressions in M, thus allowing exact analytic extrapolations to the infinite two-dimensional case (M5‘). @S1063-651X~97!05508-6# While no exact solution of lattice models for the adsorption or coadsorption of gas molecules on surfaces has been analytically derived, when first- and second-neighbor interactions between the adsorbed molecules are considered, lowtemperature numerical studies of one species of monomers adsorbed on a square lattice allow one to obtain closed-form analytic expressions for all possible phases and for the conditions under which phase transitions occur @1#. In this previous work, the surface considered was a semi-infinite M3N square lattice ( N!‘) in the presence of a gas containing one molecular species, with the adsorbed molecules each occupying one site. For this reason, we referred to them as monomers. The system is at thermal equilibrium with the monomer chemical potential energy m depending on the external gas pressure. The interaction energies of an adsorbed monomer are V0 with the lattice, V with any first-neighbor monomer at a distance a, and W with any second-neighbor monomer at a distance a&. The assumption was that the first-neighbor interaction is repulsive, V,0, allowing the second-neighbor interaction to be either attractive or repulsive. The study showed six distinct interaction regions with ‘‘p phases’’ appearing sequentially with increasing external pressure, from the empty lattice phase p0 to the fully covered lattice phase p 15 , as follows @1#.

Recent studies of one-dimensional self-gravitating systems have raised new questions about their ergodic properties, what defines equilibrium for these systems, and their ability to reach a state of thermal equilibrium in a finite time. Earlier studies of small-$N$ systems $(Nl11)$ using Lyapunov exponents have shown that stable regions exist in the phase space which prevent these systems from thermalizing. Here we investigate several small-$N$ systems with specific initial states in an attempt to answer some of the questions of ergodicity and relaxation toward equilibrium which have been sparked by recent large-$N$ $(N=64)$ simulations. Using time averages of the specific particle energy deviations from equipartition, we see similar peaks occurring in the data for small-$N$ simulations as have been reported for large $N.$ Instead of being an indication of the onset of equilibrium, these peaks may indicate regions of the phase space where the system resides for extremely long periods of time. The existence of sticky regions in the phase space in both small- and large-$N$ systems raises questions about the structure of the phase space, relaxation, and the appropriateness of various tests of equilibrium. Here we show that equipartition is not sufficient to remove fundamental doubts concerning the system's ergodic properties.