Thermodynamic Curvature of AdS Black Holes with Dark Energy

In this paper, we study the effect of dark energy on the extended thermodynamic structure and interacting microstructures of black holes in AdS, through an analysis of thermodynamic geometry. Considering various limiting cases of the novel equation of state obtained in charged rotating black holes with quintessence, and taking enthalpy H as the key potential in the extended phase space, we scrutinize the behavior of the Ruppeiner curvature scalar R in the entropy-pressure (S,P)-plane (or equivalently in the temperature-volume (T,V)-plane). Analysis of R empirically reveals that dark energy parameterized by α, significantly alters the dominant interactions of neutral, charged and slowly rotating black hole microstructures. In the Schwarzschild-AdS case: black holes smaller than a certain size continue to have attractive interactions whereas larger black holes are completely dominated by repulsive interactions which arise to due dark energy. For charged or rotating AdS black holes with quintessence, R can change sign at multiple points depending upon the relation between α and charge q or angular momentum J. In particular, above a threshold value of α, R is never negative at all, suggesting heuristically that the repulsive interactions due to quintessence are long ranged as opposed to the previously known short ranged repulsion in charged AdS black holes. A mean field interaction potential is proposed whose extrema effectively capture the points where the curvature R changes sign.

Modelling Thermally Induced Non-Equilibrium Gas Flows by Coupling Kinetic and Extended Thermodynamic Methods

Thermally induced non-equilibrium gas flows have been simulated in the present study by coupling kinetic and extended thermodynamic methods. Three different types of thermally induced gas flows, including temperature-discontinuity- and temperature-gradient-induced flows and radiometric flow, have been explored in the transition regime. The temperature-discontinuity-induced flow case has shown that as the Knudsen number increases, the regularised 26 (R26) moment equation system will gradually loss its accuracy and validation. A coupling macro- and microscopic approach is employed to overcome these problems. The R26 moment equations are used at the macroscopic level for the bulk flow region, while the kinetic equation associated with the discrete velocity method (DVM) is applied to describe the gas close to the wall at the microscopic level, which yields a hybrid DVM/R26 approach. The numerical results have shown that the hybrid DVM/R26 method can be faithfully used for the thermally induced non-equilibrium flows. The proposed scheme not only improves the accuracy of the results in comparison with the R26 equations, but also extends their capability with a wider range of Knudsen numbers. In addition, the hybrid scheme is able to reduce the computational memory and time cost compared to the DVM.

Non-equilibrium thermal transport and entropy analyses in rarefied cavity flows

Thermal transport in rarefied flows far removed from thermodynamic equilibrium is investigated using kinetic-theory-based numerical simulations. Two numerical schemes – unified gas kinetic scheme (UGKS) and direct simulation Monte Carlo (DSMC) – are employed to simulate transport at different degrees of rarefaction. Lid-driven cavity flow simulations of argon gas are performed over a range of Knudsen numbers, Mach numbers and cavity shapes. Thermal transport is then characterized as a function of lid Mach number and Knudsen number for different cavity shapes. Vast deviations from the Fourier law – including thermal transport aligned along the direction of temperature gradient – are observed. Entropy implications are examined using Sackur–Tetrode and Boltzmann $H$-theorem formulations. At low Knudsen and Mach numbers, thermal transport is shown to be amenable to both entropy formulations. However, beyond moderate Knudsen and Mach numbers, thermal transport complies only with the Boltzmann $H$-theorem entropy statement. Two extended thermodynamic models are compared against simulation data and found to account for some of the observed non-equilibrium behaviour.

Phase Transition of RN-AdS Black Hole with Fixed Electric Charge and Topological Charge

Phase transition of RN-AdS black hole is investigated from a new perspective. Not only is the cosmological constant treated as pressure but also the spatial curvature of black hole is treated as topological charge ϵ. We obtain the extended thermodynamic first law from which the mass is naturally viewed as enthalpy rather than internal energy. In canonical ensemble with fixed topological charge and electric charge Q, interesting van der Waals like oscillatory behavior in T-S and P-V graphs and swallow tail behavior in G-T and G-P graphs is observed. By applying the Maxwell equal area law and analysing the Gibbs free energy, we obtain analytical phase transition coexistence curves which are consistent with each other. The phase diagram is four dimensional with T,P,Q,ϵ.

Solubility and hydrolysis of Tc(iv) in dilute to concentrated KCl solutions: an extended thermodynamic model for Tc4+–H+–K+–Na+–Mg2+–Ca2+–OH−–Cl−–H2O(l) mixed systems

The solubility of Tc(iv) under strongly reducing conditions is investigated in KCl solutions with 1.5 ≤ pHm ≤ 14.5, and an extended thermodynamic model for the system Tc4+–H+–K+–Na+–Mg2+–Ca2+–OH−–Cl−–H2O(l) is provided.