Narrow Results

The original formulation of the Bohr–van Leeuwen (BvL) theorem states that, in a uniform magnetic field and in thermal equilibrium, the magnetization of an electron gas in the classical Drude–Lorentz model vanishes identically. This stems from classical statistics which assign the canonical momenta all values ranging from -∞ to ∞ that makes the free energy density magnetic-field-independent. When considering a classical (Maxwell–Boltzmann) interacting electron gas, it is usually admitted that the BvL theorem holds upon condition that the potentials modeling the interactions are particle-velocities-independent and do not cause the system to rotate after turning on the magnetic field. From a rigorous viewpoint, when treating large macroscopic systems, one expects the BvL theorem to hold provided the thermodynamic limit of the free energy density exists (and the equivalence of ensemble holds). This requires suitable assumptions on the many-body interactions potential and on the possible external potentials to prevent the system from collapsing or flying apart. Starting from quantum statistical mechanics, the purpose of this paper is to give, within the linear-response theory, a proof of the BvL theorem in the semiclassical limit when considering a dilute electron gas in the canonical conditions subjected to a class of translational invariant external potentials.

We discuss thermodynamic stability of neutral real (quantum) matter from the point of view of a computer experiment at finite, nonzero, temperature. We perform (restricted) path integral Monte Carlo simulations of the two component plasma where the two species are both bosons, both fermions, and one boson and one fermion. We calculate the structure of the plasma and discuss about the formation of binded couples of oppositely charged particles. The purely bosonic case is thermodynamically unstable. In this case we find an undetermined size-dependent contact value unlike partial radial distribution function. For the purely fermionic case, we find a demixing transition with binding also of like species.

Laws of thermodynamics have been examined for the universe filled with a perfect fluid, obeying an adiabatic equation of state p = γρ-A/ρ^α (called modified Chaplygin gas), where γ, A and α are positive constants and ρ and p are energy density and thermodynamic pressure respectively. Using general thermodynamics, the behavior of temperature and the thermodynamic stability has been discussed for modified Chaplygin gas. A scenario is obtained such that the thermal equation of state depends on both temperature and volume and there will be thermodynamic stability during the expansion process so that the fluid cools down through the expansion without any phase transition (or passing through any critical point).

In this paper, we have studied thermodynamics of a black hole in massive gravity in the canonical ensemble. The massive gravity theory in consideration here has a massive graviton due to Lorentz symmetry breaking. The black hole studied here has a scalar charge due to the massive graviton and is asymptotically anti-de Sitter (AdS). We have computed various thermodynamical quantities such as temperature, specific heat and free energy. Both the local and global stability of the black hole are studied by observing the behavior of the specific heat and the free energy. We have observed that there is a first-order phase transition between small (SBH) and large black hole (LBH) for a certain range of the scalar charge. This phase transition is similar to the liquid/gas phase transition at constant temperature for a van der Waals fluid. The coexistence curves for the SBH and LBH branches are also discussed in detail.

In this paper, we study the solutions of Einstein’s field equations in Einstein–Maxwell-dilaton gravity. By presenting the (3+1)-dimensional action in which gravity is coupled to a dilaton field, we derive the field equations. We present a new class of charged dilaton black hole solutions in Einstein–Maxwell-dilaton theory and investigate the effects of dilaton field on the properties of space–time. We show that these solutions are physical and describe spherically symmetric charged black holes. The calculated potential is Liouville type and has two rules. The exact solution of the field equations leads to the production of the metric function with three rules. By examining the physical properties of the solutions, we find the mass, charge, electric potential and temperature of charged dilaton black holes. Also, with the help of the canonical ensemble method, we study the thermodynamics and thermal stability of solutions and show the effects of dilaton and Maxwell fields on the thermodynamics of these solutions. Finally, by examining the phase transition of the solutions, we present thermal stability of the black hole in (3+1)-dimensional.

The XTiO₃ (X = Mn, Fe, Co and Ni) materials with R3c structure could be grown under critical conditions based on first-principles calculations and thermodynamic stability analysis. FeTiO₃ and MnTiO₃ could be synthesized relatively easily under metal-rich and O-poor conditions, while NiTiO₃ could be stable under Ni-rich, O-rich and Ti-poor conditions. The predicted R3c CoTiO₃ under thermodynamic equilibrium conditions is suggested to be synthesized under Co-rich, O-rich and Ti-poor conditions, but the calculated phonon dispersion indicates R3c CoTiO₃ becomes unstable under the dynamical conditions. The ferroelectric behavior in the XTiO₃ (X = Mn, Fe, Co and Ni) system could be dominated by the Ti ion with d⁰ state and the strong hybridization between Ti and O, while the magnetic property is mainly caused by the contribution of 3d transition metal.

In two frameworks, we discuss the thermodynamic stability of noncommutative geometry inspired Schwarzschild black hole (NCSBH). Under the horizon thermodynamics of black holes, we show that the NCSBH cannot be thermodynamically stable if requiring positive temperature. We note the inconsistency in the work of Larrañaga et al. and propose an effective first law of black hole thermodynamics for the NCSBH to eliminate the inconsistency. Based on the effective first law, we recalculate the heat capacity and the thermodynamic curvature by means of geometrothermodynamics (GTD) to revisit the thermodynamic stability.

We study the thermodynamic properties of the black hole derived in Hořava–Lifshitz (HL) gravity without the detailed-balance condition. The parameter $\mathrm{\Xi }={𝜖}^2$ in the HL black hole plays the same role as that of the electric charge in the Reissner–Nordström-anti-de Sitter (RN-AdS) black hole. By analogy, we treat the parameter $\mathrm{\Xi }$ as the thermodynamic variable and obtain the first law of thermodynamics for the HL black hole. Although the HL black hole and the RN-AdS black hole have the similar mass and temperature, due to their very different entropy, the two black holes have very different thermodynamic properties. By calculating the heat capacity and the free energy, we analyze the thermodynamic stability of the HL black hole.

The thermodynamic stability of a thin-shell wormhole in a Schwarzschild bulk is considered. From the first law, entropy function is found which satisfies the local intrinsic stability conditions. Heat capacity emerges as a well-defined regular function justifying the stability of a Schwarzschild thin-shell wormhole. Our method applies only to static thin-shell wormholes and in this sense it may be considered as supplementary to the classical method of stability. The scope of applications of the method is not limited by the Schwarzschild wormhole.