Information Equation of State

Landauer's principle is applied to information in the universe. Once stars began forming, the increasing proportion of matter at high stellar temperatures compensated for the expanding universe to provide a near constant information energy density. The information equation of state was close to the dark energy value, w = -1, for a wide range of redshifts, 10> z >0.8, over one half of cosmic time. A reasonable universe information bit content of only 10^87 bits is sufficient for information energy to account for all dark energy. A time varying equation of state with a direct link between dark energy and matter, and linked to star formation in particular, is clearly relevant to the cosmic coincidence problem.In answering the "Why now?" question we wonder "What next?" as we expect the information equation of state to tend towards w = 0 in the future.Comment: 10 pages, 2 figure

Thermal Equation of State of Tantalum

We have investigated the thermal equation of state of tantalum from first principles using the Linearized Augmented Plane Wave (LAPW) and pseudopotential methods for pressures up to 300 GPa and temperatures up to 10000 K. The equation of state at zero temperature was computed using LAPW. For finite temperatures, mixed basis pseudopotential computations were performed for 54 atom supercells. The vibrational contributions were obtained by computing the partition function using the particle in a cell model, and the the finite temperature electronic free energy was obtained from the LAPW band structures. We discuss the behavior of thermal equation of state parameters such as the Gr\"uneisen parameter $\gamma$, $q$, the thermal expansivity $\alpha$, the Anderson-Gr\"uneisen parameter $\delta_T$ as functions of pressure and temperature. The calculated Hugoniot shows excellent agreement with shock-wave experiments. An electronic topological transition was found at approximately 200 GPa

Interpolation of equation-of-state data

Aims. We use Hermite splines to interpolate pressure and its derivatives simultaneously, thereby preserving mathematical relations between the derivatives. The method therefore guarantees that thermodynamic identities are obeyed even between mesh points. In addition, our method enables an estimation of the precision of the interpolation by comparing the Hermite-spline results with those of frequent cubic (B-) spline interpolation. Methods. We have interpolated pressure as a function of temperature and density with quintic Hermite 2D-splines. The Hermite interpolation requires knowledge of pressure and its first and second derivatives at every mesh point. To obtain the partial derivatives at the mesh points, we used tabulated values if given or else thermodynamic equalities, or, if not available, values obtained by differentiating B-splines. Results. The results were obtained with the grid of the SAHA-S equation-of-state (EOS) tables. The maximum $lg P$ difference lies in the range from $10^{-9}$ to $10^{-4}$, and $\Gamma_1$ difference varies from $10^{-9}$ to $10^{-3}$. Specifically, for the points of a solar model, the maximum differences are one order of magnitude smaller than the aforementioned values. The poorest precision is found in the dissociation and ionization regions, occurring at $T \sim 1.5\cdot 10^3 - 10^5$ K. The best precision is achieved at higher temperatures, $T>10^5$ K. To discuss the significance of the interpolation errors we compare them with the corresponding difference between two different equation-of-state formalisms, SAHA-S and OPAL 2005. We find that the interpolation errors of the pressure are a few orders of magnitude less than the differences from between the physical formalisms, which is particularly true for the solar-model points.Comment: Accepted for publication in A&

Equation of State and Collective Dynamics

This talk summarizes the present status of a program to quantitatively relate data from the Relativistic Heavy Ion Collider (RHIC) on collective expansion flow to the Equation of State (EOS) of hot and dense strongly interacting matter, including the quark-gluon plasma and the quark-hadron phase transition. The limits reached with the present state of the art and the next steps required to make further progress will both be discussed.Comment: 8 pages, 6 two-part figures. Invited talk given at the 5th International Conference on the Physics and Astrophysics of Quark-Gluon Plasma (ICPAQGP 2005), Kolkata (India), Feb 8-12, 2005. Proceedings to be published in Journal of Physics: Conference Series (Jan-E Alam et al., eds.

Kinetic equation consistent with the equation of state of nuclear matter

A kinetic equation which combines the quasiparticle drift of Landau's equation with a dissipation governed by a nonlocal and noninstant scattering integral in the spirit of Snider's equation for gases is derived. Consequent balance equations for the density, momentum and energy include quasiparticle contributions and the second order quantum virial corrections. The medium effects on binary collisions are shown to mediate the latent heat, i.e., an energy conversion between correlation and thermal energy. An implementation to heavy ion collisions is discussed