Local Equation Of State Research Articles

Phase transitions in local equation-of-state approximation and anomalies of spatial charge profiles in non-uniform plasma

Impressive appearance of discontinuities in equilibrium spatial charge profiles in non-uniform Coulomb systems is under discussions in wide number of thermoelectrostatics problems. Such discontinuities are considered as peculiar micro-level manifestation of phase transitions and intrinsic macro-level non-ideality effects in local equation of state (EOS), which should be used for description of non-ideal ionic subsystem in frames of local-density (or “pseudofluid”, or “jellium” etc) approximation. Such discontinuities were discussed already by the authors for electronic subsystems. Special emphasis is made in present paper on the mentioned above non-ideality effects in non-uniform ionic subsystems, such as micro-ions profile within screening “cloud” around macro-ion in complex (dusty, colloid etc) plasmas, equilibrium charge profile in ionic traps or (and) in the neighborhood vicinity of “charged wall” etc). Multiphase EOS for simplified ionic model of classical charged hard spheres on uniformly compressible electrostatic compensating background was constructed and several illustrative examples of discussed discontinuous ionic profiles were calculated.

Local equations of state in nonequilibrium heterogeneous physicochemical systems

Equations describing local thermal and caloric equations of state in heterogeneous systems at any degree of their states’ deviation from equilibrium are derived. The state of a system is described by equations of the transfer of mixture components; these generalize the equations of classical non-equilibrium thermodynamics for strongly nonequilibrium processes. The contributions from reactions and external fields are taken into account. The equations are derived using the lattice gas model with discrete molecular distributions in space (on a scale comparable to molecular dimensions) and continuous molecular distributions (at short distances inside cells) during their translational and vibrational motions. For simplicity, it is assumed that distinctions between the sizes of mixture components are small. Contributions from potential functions of intermolecular interaction (of the Lennard-Jones type) to some coordination spheres are considered. The theory provides a unified description of the dynamics of distributions of concentrations and pair functions of mixture components in three aggregate states, and at their interfaces. Universal expressions for the local components of the pressure tensor and internal energy inside multicomponent bulk phases and at their interfaces are obtained. Local components of the pressure tensor and the internal energy are universally expressed through local unary and pair distribution functions (DFs) in any nonequilibrium state. The time evolution of the unary and pair DFs themselves is determined from the derived system of equations of mass, momentum, and energy transfer that ensure the transition of the system from a strongly nonequilibrium state to both the local equilibrium state described within traditional nonequilibrium thermodynamics and the complete thermodynamic equilibrium state postulated by classical thermodynamics.

What is the entropy in entropic gravity?

We investigate theories in which gravity arises as a consequence of entropy. We distinguish between two approaches to this idea: holographic gravity, in which Einstein's equation arises from keeping entropy stationary in equilibrium under variations of the geometry and quantum state of a small region, and thermodynamic gravity, in which Einstein's equation emerges as a local equation of state from constraints on the area of a dynamical lightsheet in a fixed spacetime background. Examining holographic gravity, we argue that its underlying assumptions can be justified in part using recent results on the form of the modular energy in quantum field theory. For thermodynamic gravity, on the other hand, we find that it is difficult to formulate a self-consistent definition of the entropy, which represents an obstacle for this approach. This investigation points the way forward in understanding the connections between gravity and entanglement.

Experimental study on the local equation of state for vibrated granular gases

We experimentally measure the local equation of state for two-dimensional horizontal fluidize granular gases confined in a rectangle box. Local equation of state can be seen as a local constitutive equation of temperature, pressure and the number density. Except the kinetic parts, the collision parts of the stress tensor are included. The diagonal components of the stress tensor are almost constant, which is consistent with the results from the simulation and hydrodynamic theory. Furthermore, the spacial profiles of the temperature and the number density are shown to be consistent with the experimental results of micro-gravity. Finally the local equations of state for different area fractions are found to have great discrepancies with the theoretical predictions no matter how the low or dense the density is.

Nonaffine heterogeneities and droplet fluctuations in an equilibrium crystalline solid

We show, using molecular-dynamics simulations, that a two-dimensional Lennard-Jones solid exhibits droplet fluctuations characterized by nonaffine deviations from local crystallinity. The fraction of particles in these droplets increases as the mean density of the solid decreases and approaches ≈20% of the total number in the vicinity of the fluid-solid phase boundary. We monitor the geometry, local equation of state, density correlations, and Van Hove functions of these droplets. We provide evidence that these nonaffine heterogeneities should be interpreted as being droplet fluctuations from nearby metastable minima. The local excess pressure of the droplets plotted against the local number density shows a van der Waal loop with distinct branches corresponding to fluidlike compact and stringlike glassy droplets. The distinction between fluidlike and glassy droplets disappears above a well-defined temperature.

Phase transition in Schwarzschild-de Sitter spacetime

Using a static massive spherically symmetric scalar field coupled to gravity in the Schwarzschild-de Sitter (SdS) background, first we consider some asymptotic solutions near horizon and their local equations of state (E.O.S.) on them. We show that near cosmological and event horizons our scalar field behaves as a dust. At the next step near two pure de Sitter or Schwarzschild horizons we obtain a coupling dependent pressure to energy density ratio. In the case of a minimally coupling this ratio is −1 which springs to the mind thermodynamical behavior of dark energy. If having a negative pressure behavior near these horizons we concluded that the coupling constant must be ξ<¼. Therefore we derive a new constraint on the value of our coupling ξ. These two different behaviors of unique matter in the distinct regions of spacetime at present era can be interpreted as a phase transition from dark matter to dark energy in the cosmic scales and construct a unified scenario.

Metastable phase equilibria in a Lennard-Jones system

A method of molecular dynamics is used to calculate the pressure, internal energy, and isochoric heat capacity in a system of 2048 Lennard-Jones particles in the range of reduced temperatures from 0.1 to 2.0 and the range of densities from 0.001 to 1.15. Local equations of state for the gas, liquid, and crystalline phases are derived. The spinodals of a superheated (extended) liquid, supersaturated vapor, and superheated (extended) crystal are determined. It is shown that the spinodal of a supercooled liquid is nonexistent. An algorithm to calculate the lines of phase equilibria is constructed. The lines of liquid-gas, liquid-crystal, crystal-gas phase equilibria, and their metastable extensions are determined. It is shown that the metastable extensions of the melting and sublimation lines terminate at the spinodals of the liquid and crystal, respectively. The properties of final critical points in the lines of melting and sublimation are considered.

Cracking of Self-Gravitating Compact Objects with Local and Non Local Equations of State

We discuss the effect that small fluctuations of density and local anisotropy (principal unequal stresses) may have on the occurrence of cracking in spherical compact objects having a non local and local politropic equations of state. A non local equation of state provides, at a given point, the radial pressure not only as function of the density at that point, but its functional throughout the enclosed distribution. It is shown that departures from the equilibrium may lead to the appearance of cracking and it seams to be related not only to fluctuations on the local anisotropy but also to the density. We have found that these fluctuations should have the same sign and the effect of the perturbations in density qualitatively different to the variations in anisotropy.

Local equation of state and velocity distributions of a driven granular gas

We present event-driven simulations of a granular gas of inelastic hard disks with incomplete normal restitution in two dimensions between vibrating walls (without gravity). We measure hydrodynamic quantities such as the stress tensor, density and temperature profiles, as well as velocity distributions. Relating the local pressure to the local temperature and local density, we construct a local constitutive equation. For strong inelasticities the local constitutive relation depends on global system parameters, like the volume fraction and the aspect ratio. For moderate inelasticities the constitutive relation is approximately independent of the system parameters and can hence be regarded as a local equation of state, even though the system is highly inhomogeneous with heterogeneous temperature and density profiles arising as a consequence of energy injection. With respect to local velocity distributions we find that they do not scale with the square root of the local granular temperature. Moreover the high-velocity tails are different for the distribution of the x and the y components of the velocity, and even depend on the position in the sample, the global volume fraction, and the coefficient of restitution.

Phase transitions in gravitating systems and the formation of condensed objects

The thermal equilibrium of a self-gravitating classical fluid with local equation of state corresponding to a system of hard spheres is studied numerically. When the volume effectively occupied by the particles is much smaller than the accessible volume, a phase transition occurs at which the system can shuttle between a quasi-uniform state and one in which a highly condensed nucleus is immersed in a dilute atmosphere. Under isothermal contact conditions, the two states have different energies; under isoenergetic conditions, they have different temperatures. The isothermal transition bridges a region of negative specific heat in the family of isoenergetic systems. The phase transitions mark nonlinear fluid stability thresholds. These can differ by orders of magnitude from the traditional linear ones, i.e. the gravothermal catastrophe and Jeans instability, which only mark the stability limits of thermally metastable regions. It is discussed how phase transitions may give the proper onset criteria for the formation of condensed objects from the size of planetoids up to stars.

Turbulent magnetohydrodynamic density fluctuations

A spectral-method numerical code is used to compute mass-density fluctuation spectra in turbulent magnetofluids. The computations are used to test and extend a recent analytical theory of density variations in slightly compressible magnetofluids given by Montgomery, Brown and Matthaeus, and used by them to infer inertial-range density-fluctuation spectra for the nearby interstellar medium and solar wind. A local equation of state is assumed, relating density to pressure. Constant, scalar resistivities and viscosities are used. In the limit of low Mach numbers and high mechanical-to-magnetic pressure ratios, the fit of the computations to the analytical theory is seen to be close.

Thermodynamics and general relativity could determine the geometry of the universe

We introduce a suggestive model where certain quantities in Friedmann models are treated like their thermodynamic counterparts; temperature entropy, Gibbs energy, and so on. Within this model, changes in the symmetry of the universe are interpreted as first- or second-order phase transitions. The thermodynamics we introduce give us a new way of determining the geometry of the universe. By choosing a specific local equation of state (P=αρ), we show that with respect to the thermodynamics we have introduced, it is always more advantageous for the universe to be in a Bianchi V (open) symmetric state.

Thermodynamics and General Relativity Could Determine the Symmetry of the Universe

We introduce a suggestive model where certain quantities in Friedmann models are treated like their thermodynamic counterparts; temperature entropy, Gibbs energy, and so on. Within this model, changes in the symmetry of the universe are interpreted as first- or second-order phase transitions. The thermodynamics we introduce give us a new way of determining the geometry of the universe. By choosing a specific local equation of state (P=αρ), we show that with respect to the thermodynamics we have introduced, it is always more advantageous for the universe to be in a Bianchi V (open) symmetric state.