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The vast majority of materials shrink in all directions when hydrostatically compressed; exceptions include certain metallic or polymer foam structures, which may exhibit negative linear compressibility (NLC) (that is, they expand in one or more directions under hydrostatic compression). Materials that exhibit this property at the molecular level--crystalline solids with intrinsic NLC--are extremely uncommon. With the use of neutron powder diffraction, we have discovered and characterized both NLC and extremely anisotropic thermal expansion, including negative thermal expansion (NTE) along the NLC axis, in a simple molecular crystal (the deuterated 1:1 compound of methanol and water). Apically linked rhombuses, which are formed by the bridging of hydroxyl-water chains with methyl groups, extend along the axis of NLC/NTE and lead to the observed behavior.

CompOSE (CompStar Online Supernovae Equations of State) is an online repository of equations of state (EoS) for use in nuclear physics and astrophysics, e.g., in the description of compact stars or the simulation of core-collapse supernovae and neutron-star mergers, see https://compose.obspm.fr. The main services, offered via the website, are: a collection of data tables in a flexible and easily extendable data format for different EoS types and related physical quantities with extensive documentation and referencing; software for download to extract and to interpolate these data and to calculate additional quantities; webtools to generate EoS tables that are customized to the needs of the users and to illustrate dependencies of various EoS quantities in graphical form. This manual is an update of previous versions that are available on the CompOSE website, at arXiv:1307.5715 [astro-ph.SR], and that was originally published in the journal “Physics of Particles and Nuclei” with doi:10.1134/S1063779615040061. It contains a detailed description of the service, containing a general introduction as well as instructions for potential contributors and for users. Short versions of the manual for EoS users and providers will also be available as separate publications. Graphical Abstract

Eulerian finite strain of an elastically isotropic body is defined using the expansion of squared length and the post-compression state as reference. The key to deriving second-, third- and fourth-order Birch–Murnaghan equations-of-state (EOSs) is not requiring a differential to describe the dimensions of a body owing to isotropic, uniform, and finite change in length and, therefore, volume. Truncation of higher orders of finite strain to express the Helmholtz free energy is not equal to ignoring higher-order pressure derivatives of the bulk modulus as zero. To better understand the Eulerian scheme, finite strain is defined by taking the pre-compressed state as the reference and EOSs are derived in both the Lagrangian and Eulerian schemes. In the Lagrangian scheme, pressure increases less significantly upon compression than the Eulerian scheme. Different Eulerian strains are defined by expansion of linear and cubed length and the first- and third-power Eulerian EOSs are derived in these schemes. Fitting analysis of pressure-scale-free data using these equations indicates that the Lagrangian scheme is inappropriate to describe P-V-T relations of MgO, whereas three Eulerian EOSs including the Birch–Murnaghan EOS have equivalent significance.

A bstract We determine the QCD equation of state at nonzero temperature in the presence of an isospin asymmetry between the light quark chemical potentials on the lattice. Our simulations employ N f = 2 + 1 flavors of dynamical staggered quarks at physical masses, using three different lattice spacings. The main results, obtained at the individual lattice spacings, are based on a two-dimensional spline interpolation of the isospin density, from which all relevant quantities can be obtained analytically. In particular, we present results for the pressure, the interaction measure, the energy and entropy densities, as well as the speed of sound. Remarkably, the latter is found to exceed its ideal gas limit deep in the pion condensed phase, the first account of the violation of this limit in first principles QCD. Finally, we also compute the phase diagram in the temperature — isospin density plane for the first time. Even though the results are not continuum extrapolated and thus not final, the data for all observables will be useful for the benchmarking of effective theories and low-energy models of QCD and are provided in ancillary files for simple reuse.

As one of few who have been involved in the equation of state of seawater over the last 40 years, I was invited to review some of the history behind its early development and also the more recent thermodynamic equation of state. The article first reviews early (late 1800s) work by Knudsen and others in defining the concept of salinity. This summary leads into the development of the practical salinity scale. Our studies at the University of Miami Rosenstiel School, along with the work of Alain Poisson's group at Laboratoire de Physique et Chimie, Université Pierre et Marie Curie, and that of Alvin Bradshaw and Karl Schleicher at Woods Hole Oceanographic Institution, were instrumental in deriving the 1980 equation of state (EOS-80) that has been used for 30 years. The fundamental work of Ranier Feistel at Leibniz Institute for Baltic Sea Research led to the development of a Gibbs free energy function that is the backbone of the new thermodynamic equation of state (TEOS-10). It can be used to determine all of the thermodynamic properties of seawater. The salinity input to the TEOS-10 Gibbs function requires knowledge of the absolute salinity of seawater (SA), which is based upon the reference salinity of seawater (SR). The reference salinity is our best estimate of the absolute salinity of the seawater that was used to develop the practical salinity scale (SP), the equation of state, and the other thermodynamic properties of seawater. Reference salinity is related to practical salinity by SR= SP(35.16504/35.000) g kg⁻¹ and absolute salinity is related to reference salinity by SA= SR+ δSA, where δSAis due to the added solutes in seawater in deep waters resulting from the dissolution of CaCO₃(s) and SiO₂(s), CO₂, and nutrients like NO₃ and PO₄ from the oxidation of plant material. The δSAvalues due to the added solutes are estimated from the differences between the measured densities of seawater samples compared with the densities calculated from the TEOS-10 equation of state (Δρ) at the same reference salinity, temperature, and pressure, using δSA= Δρ/0.75179 g kg⁻¹. The values of δSAin the ocean can be estimated for waters at given longitude, latitude, and depth using correlations of δSAand the concentration of Si(OH)₄ in the waters. The SAvalues can then be used to calculate all the thermodynamic properties of seawater in the major oceans using the new TEOS-10. It will be very useful to modelers examining the entropy and enthalpy of seawater.

A bstract The equation of state of neutron-star cores can be constrained by requiring a consistent connection to the perturbative Quantum Chromodynamics (QCD) calculations at high densities. The constraining power of the QCD input depends on uncertainties from missing higher-order terms, the choice of the unphysical renormalization scale, and the reference density where QCD calculations are performed. Within a Bayesian approach, we discuss the convergence of the perturbative QCD series, quantify its uncertainties at high densities, and present a framework to systematically propagate the uncertainties down to neutron-star densities. We find that the effect of the QCD input on the neutron-star inference is insensitive to the various unphysical choices made in the uncertainty estimation.

The Tolman–Oppenheimer–Volkoff (TOV) equations govern the radial evolution of pressure and energy density in static neutron stars (NSs) in hydrodynamical equilibrium. Using the reduced pressure and energy density with respect to the NS central energy density, the original TOV equations can be recast into dimensionless forms. While the traditionally used integral approach for solving the original TOV equations require an input nuclear Equation of State (EOS), the dimensionless TOV equations can be anatomized by using the reduced pressure and energy density as polynomials of the reduced radial coordinate without using any input nuclear EOS. It has been shown in several of our recent works that interesting and novel perspectives about NS core EOS can be extracted directly from NS observables by using the latter approach. Our approach is based on i ntrinsic and p erturbative a nalyses of the d imensionless (IPAD) TOV equations (IPAD-TOV). In this review article, we first discuss the length and energy density scales of NSs as well as the dimensionless TOV equations for scaled variables and their perturbative solutions near NS cores. We then review several new insights into NS physics gained from solving perturbatively the scaled TOV equations. Whenever appropriate, comparisons with the traditional approach from solving the original TOV equations will be made. In particular, we first show that the nonlinearity of the TOV equations basically excludes a linear EOS for dense matter in NS cores. We then show that perturbative analyses of the scaled TOV equations enable us to reveal novel scalings of the NS mass, radius and the compactness with certain combinations of the NS central pressure and energy density. Thus, observational data on either mass, radius or compactness can be used to constrain directly the core EOS of NS matter independent of the still very uncertain nuclear EOS models. As examples, the EOS of the densest visible matter in our Universe before the most massive neutron stars collapse into black holes (BHs) as well as the central EOS of a canonical or a 2.1 solar mass NS are extracted without using any nuclear EOS model. In addition, we show that causality in NSs sets an upper bound of about 0.374 for the ratio of pressure over energy density and correspondingly a lower limit for trace anomaly in supra-dense matter. We also demonstrate that the strong-field gravity plays a fundamental role in extruding a peak in the density/radius profile of the speed of sound squared (SSS) in massive NS cores independent of the nuclear EOS. Finally, some future perspectives of NS research using the new approach reviewed here by solving perturbatively the dimensionless TOV equations are outlined.

A bstract QCD phase diagram in the T − μ plane and the equation of state for pure gluon, 2-flavor, 2+1-flavor systems, and 2+1+1-flavor systems have been investigated using the Einstein-Maxwell-Dilaton (EMD) framework at finite temperature and chemical potential. By inputting lattice QCD data for the equation of state and baryon number susceptibility at zero chemical potential into holographic model, all the parameters can be determined with the aid of machine learning algorithms. Our findings indicate that the deconfinement phase transition is of first order for the pure gluon system with critical temperature T c = 0.265 GeV at vanishing chemical potential. The phase transition for the 2-flavor, 2+1-flavor systems, and 2+1+1-flavor systems are crossover at vanishing chemical potential and first-order at high chemical potential, and the critical endpoint (CEP) in the T − μ plane locates at ( μ B c = 0.46 GeV, T c = 0.147 GeV), ( μ B c = 0.74 GeV, T c = 0.094 GeV), and ( μ B c = 0.87 GeV, T c = 0.108 GeV), respectively. Additionally, the thermodynamic quantities of the system for different flavors at finite chemical potential are presented in this paper. It is observed that the difference between the 2+1-flavor and 2+1+1-flavor systems is invisible at vanishing chemical potential and low temperature. The location of CEP for 2+1+1-flavor system deviates explicitly from that of the 2+1-flavor system with the increase of chemical potential. Both 2+1-flavor and 2+1+1-flavor systems differ significantly from the 2-flavor system. Moreover, at zero temperature, the critical chemical potential is found to be μ B = 1.1 GeV, 1.6 GeV, 1.9 GeV for the 2-flavor, 2+1-flavor and 2+1+1-flavor systems, respectively.

Isobaric heat capacity is one of the key thermophysical properties for working fluids in thermal systems and plays an important role in the development of equation of state. Due to the lack of experimental data for promising hydrofluoroolefins (HFOs), we carried out theoretical predictions for condensed liquid phase with three different methods: traditional cubic equation of state (CEOS), fundamental equations of state (FEOS) explicit in Helmholtz free energy and a corresponding state equation (CSE). Both CEOS and CSE are generalized models that only need several characteristic parameters to conduct calculation, while FEOS are specific models in which the structure and parameters are regressed from experimental data of one certain fluid. Liquid heat capacity data of 9 HFOs were calculated, including well-known R1234yf, R1234ze(E), and latest prospective R1123, R1216, R1243zf, R1234ze(Z), R1336mzz(Z), R1141, and R1125zc. A critical comparison was carried out between different calculation methods. The comparison showed that both CSE and FEOS predicted available experimental data well with AADs % less than the reported experimental uncertainties. For refrigerants without experimental heat capacity, CSE and FEOS showed good agreements with AADs % less than 3.6 %. The selected CEOS always provided relatively larger predictions than experiments or the other two methods. Despite that, calculated data of CEOS showed a strong linear relation with the other two methods, which suggested that there might be a potential linear modification or correlation for CEOS in improving its heat capacity calculations. Furthermore, when there were no experimental data available, CSE used in this study could be a useful preliminary evaluation tool for the liquid heat capacity of hydrofluoroolefins, considering its accuracy and easy application characteristics.

We review the equation of state (EoS) models covering a large range of temperatures, baryon number densities and electron fractions presently available on the CompOSE database. These models are intended to be directly usable within numerical simulations of core-collapse supernovae, binary neutron star mergers and proto-neutron star evolution. We discuss their compliance with existing constraints from astrophysical observations and nuclear data. For a selection of purely nucleonic models in reasonable agreement with the above constraints, after discussing the properties of cold matter, we review thermal properties for thermodynamic conditions relevant for core-collapse supernovae and binary neutron star mergers. We find that the latter are strongly influenced by the density dependence of the nucleon effective mass. The selected bunch of models is used to investigate the EoS dependence of hot star properties, where entropy per baryon and electron fraction profiles are inspired from proto-neutron star evolution. The Γ -law analytical thermal EoS used in many simulations is found not to describe well these thermal properties of the EoS. However, it may offer a fair description of the structure of hot stars whenever thermal effects on the baryonic part are small, as shown here for proto-neutron stars starting from several seconds after bounce.