Thermodynamic Transition Research Articles

Excitation-wavelength-dependent persistent luminescence from single-component nonstoichiometric CaGaxO4:Bi for dynamic anti-counterfeiting

Materials capable of dynamic persistent luminescence (PersL) within the visible spectrum are highly sought after for applications in display, biosensing, and information security. However, PersL materials with eye-detectable and excitation-wavelength-dependent characteristics are rarely achieved. Herein, a nonstoichiometric compound CaGaxO4:Bi (x < 2) is present, which demonstrates ultra-long, color-tunable PersL. The persistent emission wavelength can be tuned by varying the excitation wavelength, enabling dynamic color modulation from the green to the orange region within the visible spectrum. Theoretical calculations, in conjunction with experimental observations, are utilized to elucidate the thermodynamic charge transitions of various defect states, thereby providing insights into the relationship between Bi3+ emitters, traps, and multicolored PersL. Furthermore, the utility of color-tunable PersL materials and flexible devices is showcased for use in visual sensing of invisible ultraviolet light, multicolor display, information encryption, and anti-counterfeiting. These discoveries create new opportunities to develop smart photoelectric materials with dynamically controlled PersL for various applications.

Sulfur fixation performance of calcium-bearing carbonates in iron ore roasting process: Thermodynamics, phase transition, microstructure evolution, and kinetics

Roasting technology is increasingly used in the beneficiation of refractory iron ores. During the roasting process, the presence of pyrite in some iron ores leads to the formation of SO2, requiring effective sulfur fixation techniques. This study proposed an innovative in-situ sulfur fixation method by pre-oxidation roasting, in which sulfur was fixed during the oxidation roasting process before reduction roasting. The effects of the main iron mineral (hematite), primary gangue mineral (quartz), and common calcium-containing carbonate minerals (calcite and dolomite) on sulfur migration during pyrite roasting were investigated, with particular emphasis on the sulfur fixation capabilities of calcite and dolomite. The study included thermodynamic equilibrium analysis, phase transitions and microstructural evolution in different reaction systems. The results showed that calcite and dolomite effectively reduced SO2 emissions by forming CaSO4 and MgSO4, with calcite exhibiting a stronger sulfur fixation capacity for the same mass. Kinetic analysis indicated that pyrite pyrolysis followed a two-step random nucleation and growth model. Furthermore, the addition of calcite increased the apparent activation energy of SO2 formation and altered the reaction pathway, providing insight into the sulfur fixation mechanism of calcite from a kinetic perspective.

From Geometry of Hamiltonian Dynamics to Topology of Phase Transitions: A Review.

In this review work, we outline a conceptual path that, starting from the numerical investigation of the transition between weak chaos and strong chaos in Hamiltonian systems with many degrees of freedom, comes to highlight how, at the basis of equilibrium phase transitions, there must be major changes in the topology of submanifolds of the phase space of Hamiltonian systems that describe systems that exhibit phase transitions. In fact, the numerical investigation of Hamiltonian flows of a large number of degrees of freedom that undergo a thermodynamic phase transition has revealed peculiar dynamical signatures detected through the energy dependence of the largest Lyapunov exponent, that is, of the degree of chaoticity of the dynamics at the phase transition point. The geometrization of Hamiltonian flows in terms of geodesic flows on suitably defined Riemannian manifolds, used to explain the origin of deterministic chaos, combined with the investigation of the dynamical counterpart of phase transitions unveils peculiar geometrical changes of the mechanical manifolds in correspondence to the peculiar dynamical changes at the phase transition point. Then, it turns out that these peculiar geometrical changes are the effect of deeper topological changes of the configuration space hypersurfaces ∑v=VN-1(v) as well as of the manifolds {Mv=VN-1((-∞,v])}v∈R bounded by the ∑v. In other words, denoting by vc the critical value of the average potential energy density at which the phase transition takes place, the members of the family {∑v}v<vc are not diffeomorphic to those of the family {∑v}v>vc; additionally, the members of the family {Mv}v>vc are not diffeomorphic to those of {Mv}v>vc. The topological theory of the deep origin of phase transitions allows a unifying framework to tackle phase transitions that may or may not be due to a symmetry-breaking phenomenon (that is, with or without an order parameter) and to finite/small N systems.

Complexity of confined water vitrification and its glass transition temperature

The ability of vitrification when crossing the glass transition temperature (Tg) of confined and bulk water is crucial for myriad phenomena in diverse fields, ranging from the cryopreservation of organs and food to the development of cryoenzymatic reactions, frost damage to buildings, and atmospheric water. However, determining water's Tg remains a major challenge. Here, we elucidate the glass transition of water by analyzing the calorimetric behavior of nano-confined water across various pore topologies (diameters: 0.3 to 2.5 nm). Our approach involves subjecting confined water to annealing protocols to identify the temperature and time evolution of nonequilibrium glass kinetics. Furthermore, we complement this calorimetric approach with the dynamics of confined water, as seen by broadband dielectric spectroscopy and linear calorimetric measurements, including the fast scanning technique. This study demonstrated that confined water undergoes a glass transition in the temperature range of 170 to 200 K, depending on the confinement size and the interaction with the confinement walls. Moreover, we also show that the thermal event observed at ~136 K must be interpreted as an annealing prepeak, also referred to as the "shadow glass transition." Calorimetric measurements also allow the detection of a specific heat step above 200 K, which is insensitive to annealing and, thereby, interpreted as a true thermodynamic transition. Finally, by connecting our results to bulk water behavior, we offer a comprehensive understanding of confined water vitrification with potential implications for numerous applications.

Molecular dynamics analysis of the crossover phenomenon in supercritical carbon dioxide

Supercritical carbon dioxide (SCO2) finds widespread applications but its complex phase behavior near and beyond the critical point remains unclear. In this work, extensive focus has been invested in the thermodynamic transitions of SCO2 from a microscopic perspective. It is revealed that both the radial distribution function and structure factor exhibit apparent crossover phenomena as temperature changes. Remarkably, our findings demonstrate an unprecedented agreement between the predicted crossover points using different functions and the experimental Frenkel Line (FL), with a deviation of merely 5.6%. By applying the same method, the FL crossover region is successfully predicted and extended up to an impressive pressure of 200 MPa. Notably, this prediction is a valuable guide in narrowing down the temperature range for further experimental tests. Concurrently, a correlation between the coordination number and the FL is discovered. Overall, our research provides compelling evidence supporting the FL as thermodynamic transitions between the gas-like and liquid-like regions and presents a novel and reliable approach for identifying the FL, which offers valuable theoretical insights into the phase behavior in the supercritical state.

Molecular-Level Understanding of Phase Stability in Phase-Change Nanoemulsions for Thermal Energy Storage by NMR Spectroscopy.

Phase change materials (PCMs) are latent heat storage materials that can store or release thermal energy while undergoing thermodynamic phase transitions. Organic PCMs can be emulsified in water in the presence of surfactants to enhance thermal conductivity and enable applications as heat transfer fluids. However, PCM nanoemulsions often become unstable during thermal cycling. To better understand the molecular origins of phase stability in PCM nanoemulsions, we designed a model PCM nanoemulsion system and studied how the molecular-level environments and dynamics of the surfactants and oil phase changed upon thermal cycling using liquid-state nuclear magnetic resonance (NMR) spectroscopy. The model system used octadecane as the oil phase, stearic acid as the surfactant, and aqueous NaOH as the continuous phase. The liquid fraction of octadecane within the nanoemulsions was quantified noninvasively during thermal cycling by liquid-state 1H single-pulse NMR measurements, revealing the extent of octadecane supercooling as a function of temperature. The mean droplet size of the PCM nanoemulsions, measured by dynamic light scattering (DLS), was correlated with the liquid content of octadecane to explain phase instability in the solid-liquid coexistence region. Quantitative 13C single-pulse NMR experiments established that the carbonyl surfactant head groups were present in multiple distinct environments during thermal cycling. After repeated thermal cycling, the 13C signal intensity of the carbonyl surfactant head groups decreased, indicating that the surfactant head groups lost molecular mobility. The results explain, in part, the origin of phase instability of PCM nanoemulsions upon thermal cycling.

Transitions between equilibrium and nonequilibrium phenomena in the description of crystal growth

The close intertwining of equilibrium and nonequilibrium thermodynamic representations and transitions between the two limiting principles of thermodynamics: the second beginning and the principle of least coercion (minimum entropy production in the stationary regime) constitute the main content of phenomenological theories of crystal growth. The difference of basic postulates of two sections of thermodynamics forces to discuss problems of reversibility and irreversibility of time, scales of observed phenomena and rules of conjugation of thermodynamic forces and flows in theories of crystal growth. A variant of the solution of some conjugation problems is shown on the example of the fluctuation model of dislocation crystal growth, which is based on the stationary isothermal process of thermodynamic free energy fluctuations. In the case of the limiting mode of adsorption of impurities on the crystal face according to the Langmuir model, the free energy fluctuations possessing the absence of the memory effect allow us to identify three chemical potentials of building particles that determine the corresponding values of solution supersaturations realized at different scale levels at the growing crystal face containing a helical dislocation. The supersaturations control quasi-equilibrium and nonequilibrium thermodynamic processes that constitute a single dislocation mechanism of crystal growth.

Re-entrant phase transitions in Laponite/Gum Arabic nanocomposites

A re-entrant gel transition is observed in a discotic clay, Laponite (Lap) aqueous suspensions with the addition of a complex polysaccharide, Gum Arabic (GA). For fixed concentrations of Lap (1–3 % w/v) and at low GA concentrations (CGA < 10 % w/v), the composites exhibit gel behaviour, while the suspensions undergo liquid phase separation for intermediate GA concentrations (10 % w/v < CGA < 20 % w/v). Gel behaviour is again observed in the samples at even higher GA concentrations (CGA > 30 % w/v). Here, we identify a thermodynamic phase transition in Lap/GA mixtures that is caused by a variation in GA content. The viscoelastic characteristics, phase transitions, and gelation kinetics of the Lap/GA mixtures have been studied by employing rheology, small-angle X-ray scattering, and optical investigations. Reduction of the negative values of zeta-potential and growth of the composite system's hydrodynamic size indicated the presence of interactions in Lap/GA mixtures. The phase diagram enables the apparent interactions and phase transitions between the nanoplatelets and the complex polysaccharides. Thus, our study provides new perspectives on a nanocomposite's tuneable rheological and structural features.

Acoustic Shock Wave-Induced Rutile to Anatase Phase Transition of TiO2 Nanoparticles and Exploration of Their Unconventional Thermodynamic Structural Transition Path of Crystallization Behaviors.

Titanium dioxide (TiO2) is one of the most well-known and long-standing polymorphic materials in the transition metal oxide group of materials. The transition from rutile to anatase is one of the long-standing fundamental questions among materials science researchers because seeking the nucleation site at the beginning of the phase transition is highly challenging. Until now, there have been no studies on the unconventional structural phase transition of TiO2 nanoparticles by acoustic shock waves. In the present study, this work provides the first evidence on the solid-state nanostructure of the rutile-to-anatase phase transition of TiO2 by acoustic shock waves whereby these phase transition results are evaluated by Raman spectroscopy, thermal calorimetry, X-ray photoelectron spectroscopy, and microscopic techniques. We propose a novel mechanism for the occurrence of the rutile-to-anatase phase transition based on thermophysical properties and shock wave-induced melting concepts. Under shocked conditions, the R-A phase transition occurs because of the anatase phase's lower interfacial energy (γL/A) and surface energy compared to rutile. We strongly believe that the present work can provide in-depth insight into understanding the crystallization concepts of the TiO2 NPs under extreme conditions, especially with regard to the rutile-to-anatase phase transition.

The ab initio study of n-type nitrogen and gallium co-doped diamond

Abstract In order to better understand the influence of different complexes on the diamond co-doping system, N and Ga are chosen as co-dopants in diamond. The properties of several substitutional NmGan (m+n &lt;= 3) complexes with vacancy (Va) in the bulk diamond have been investigated by ab initio density functional technique, including their optimized lattice structures, formation energies, binding energies and thermodynamic transition levels. The calculational results show that NmGan complexes in the donor-acceptor-donor (DAD) configuration can provide ionization energies similar to phosphorus-doped diamond. All other complexes provide deep impurity levels. For the DAD configuration, the adsorption process on the diamond surface has been studied to demonstrate the feasibility of growing diamonds containing N-Ga-N in experiments. The desired complex configuration is not uniquely present in the co-doped system. Investigating these properties of different complexes beyond NGaN provides insight into the N and Ga codoped diamond system, yielding a more comprehensive understanding of its potential and limitations. Our research ideas can also be extended to other co-doped systems and help to evaluate other potential co-dopants for diamond.

Dynamic magnetic characteristics of the kinetic Ising model under the influence of randomness.

In this paper, we propose to solve the issues of long-range or next-neighbor interactions by introducing randomness. This approach is applied to the square lattice Ising model. The Monte Carlo method with the Metropolis algorithm is utilized to calculate the critical temperature T_{C}^{*} under equilibrium thermodynamic phase transition conditions and to investigate the characterization of randomness in terms of magnetization. In order to further characterize the effect of this randomness on the magnetic system, clustering coefficients C_{p} are introduced. Furthermore, we investigate a number of dynamic magnetic behaviors, including dynamic hysteresis behaviors and metamagnetic anomalies. The results indicate that noise has the effect of destabilizing the system and promoting the dynamic phase transition. When the system is subjected to noise, the effect of this noise can be mitigated by the addition of a time-oscillating magnetic field. Finally, the evolution of anomalous metamagnetic fluctuations under the influence of white noise is examined. The relationship between the bias field corresponding to the peak of the curve h_{b}^{peak} and the noise parameter σ satisfies the exponential growth equation, which is consistent with other results.

Photon orbits and phase transitions in Kiselev-AdS black holes from f(R,T)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(R,\\; T)$$\\end{document} gravity

The acceleration observed in cosmological expansion is often attributed to negative pressure, potentially arising from quintessence. We explore the relationship between the photon orbit radius and the phase transition of spherical AdS black holes in f(R, T) gravity influenced by quintessence dark energy, specifically Kiselev-AdS black holes in f(R, T) gravity. We are treating the negative cosmological constant Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document} as the system’s pressure to examine the impact of the state parameter ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document} and the f(R, T) gravity parameter γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document}. Interestingly, Kiselev-AdS black holes within the f(R, T) gravity framework exhibit a van der Waals-like phase transition. In contrast, these black holes display a Hawking–Page-like phase transition in general relativity. We demonstrate that below the critical point, the black hole undergoes a first-order vdW-like phase transition, with rps\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_{ps}$$\\end{document} and ups\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$u_{ps}$$\\end{document} serving as order parameters exhibiting a critical exponent of 1/2, similar to ordinary thermal systems. It suggests that rps\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_{ps}$$\\end{document} and ups\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$u_{ps}$$\\end{document} can serve as order parameters in characterizing black hole phase transitions, hinting at a potentially universal gravitational relationship near critical points within black hole thermodynamic systems. Investigating the correlation between photon sphere radius and thermodynamic phase transitions provides a valuable means of distinguishing between different gravity theory models, ultimately shedding light on the nature of dark energy. Finally, as γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document} tends towards zero, our results precisely align with those of Kiselev-AdS black holes.

Prewetting couples membrane and protein phase transitions to greatly enhance coexistence in models and cells.

Both membranes and biopolymers can individually separate into coexisting liquid phases. Here we explore biopolymer prewetting at membranes, a phase transition that emerges when these two thermodynamic systems are coupled. In reconstitution, we couple short poly-L-Lysine and poly-L-Glutamic Acid polyelectrolytes to membranes of saturated lipids, unsaturated lipids, and cholesterol, and detect coexisting prewet and dry surface phases well outside of the region of coexistence for each individual system. Notability, polyelectrolyte prewetting is highly sensitive to membrane lipid composition, occurring at 10 fold lower polymer concentration in a membrane close to its phase transition compared to one without a phase transition. In cells, protein prewetting is achieved using an optogenetic tool that enables titration of condensing proteins and tethering to the plasma membrane inner leaflet. Here we show that protein prewetting occurs for conditions well outside those where proteins condense in the cytoplasm, and that the stability of prewet domains is sensitive to perturbations of plasma membrane composition and structure. Our work presents an example of how thermodynamic phase transitions can impact cellular structure outside their individual coexistence regions, suggesting new possible roles for phase-separation-prone systems in cell biology.

Thermodynamics, phase transition and Joule–Thomson expansion of 4-D Gauss–Bonnet AdS black hole

In this paper, we explore the thermodynamic and phase transition properties of asymptotically AdS black holes within Einstein–Gauss–Bonnet gravity, focusing on Joule–Thomson expansion. Thermodynamics is studied in the extended phase space, where the cosmological constant serves as thermodynamic pressure. We observe that the black hole undergoes a phase transition similar to that of a van der Waals system. We analyze charged and neutral cases separately to distinguish the effect of charge and Gauss–Bonnet parameter on critical behavior and examine the phase structure. We find that the Gauss–Bonnet coupling parameter behaves similarly to black hole charge or spin, guiding the phase structure. To understand the underlying phase structure determined by the Gauss–Bonnet coefficient [Formula: see text], we introduce a new order parameter. We discover that the change in the conjugate variable to the Gauss–Bonnet parameter acts as an order parameter, demonstrating a critical exponent of [Formula: see text] in the vicinity of the critical point. Since the phase structure is analogous to that of a van der Waals fluid, we investigate the Joule–Thomson expansion of the black hole. We analytically study the Joule–Thomson expansion, focusing on three key characteristics: the Joule–Thomson coefficient, inversion curves and isenthalpic curves. We obtain isenthalpic curves in the T–P plane and illustrate the cooling–heating regions.

Study of native point defects in Al0.5Ga0.5N by first principles calculations

To explore the formation mechanism of native point defects in high Al content AlGaN film, the first principles methods are applied to study the native point defects in Al0.5Ga0.5N. The different kinds of vacancies, interstitials, and antisites are investigated. The formation energies of Al0.5Ga0.5N with native point defects under different charge states and growth conditions are analyzed and compared. Then, the preferable charge state, donor and acceptor properties of Al0.5Ga0.5N with different native point defects are explicitly obtained. The results show that AlN, GaN, Ali, and VN exhibit donor properties in p-type condition while VGa, VAl, VN, and NGa exhibit acceptor properties and can play roles as compensating center in n-type Al0.5Ga0.5N under metal rich condition. For N rich condition,VGa, VAl, NGa, and NAl are favorable acceptors in n-type Al0.5Ga0.5N. Meanwhile, the charge distribution and bonding state of Al0.5Ga0.5N with native point defects are explored. It is found the N atoms in Ni and NGa form covalent bond and ionic bond with atoms in Al0.5Ga0.5N. Moreover, the band calculation reveals that the removal of N atom in Al0.5Ga0.5N makes the conduction band fatter and the effective masses of electrons increase while the introduction of N point defects make the valence band flatter, increasing the effective masses of holes. Furthermore, the corresponding thermodynamic transition energy levels of defects under different charge states are summarized. It is found that the thermodynamic transitions for VN, Ni, and NAl may likely to happen under certain conditions. The above studies yield a detailed and quantitative description of native point defects in Al0.5Ga0.5N, which helps to get a deeper insight to the growth and doping of AlGaN.

Thermodynamics and simulation of 3D crystals and phase transitions under external fields.

A field-supported multiphase kinetic Monte Carlo method previously applied to self-assembled trimesic acid molecular layers [Ustinov et al., Phys. Chem. Chem. Phys. 24, 26111 (2022)] was generalized to three-dimensional gas-liquid and gas-solid systems. This method allows us to calculate the thermodynamic potentials of the liquid and solid phases and then determine the parameters of the liquid-solid phase transition. In this study, the requirement that the gas phase be ideal was introduced as an additional condition. It was shown that in a two-phase system, the sum of the analytical expression for the chemical potential of an ideal gas and the external potential imposed on the gas phase exactly equals the chemical potential of the equilibrium crystal or liquid phase. For example, the coexistence of crystalline/liquid krypton and ideal gas has been considered. A comparison with previously published data has shown that the proposed approach provides the most accurate results for determining the parameters of phase transitions and fully satisfies the Gibbs-Duhem equation. This method does not impose any restrictions on the complexity or hardness of dense phases.

Is it possible to overheat ice? The activated melting of TIP4P/Ice at solid–vapour coexistence.

A widely accepted phenomenological rule states that solids with free surfaces cannot be overheated. In this work we discuss this statement critically under the light of the statistical thermodynamics of interfacial roughening transitions. Our results show that the basal face of ice as described by the TIP4P/Ice model can remain mechanically stable for more than one hundred nanoseconds when overheated by 1 K, and for several hundreds of nanoseconds at smaller overheating despite the presence of a significant quasi-liquid layer at the surface. Such time scales, which are often of little experimental significance, can become a concern for the determination of melting points by computer simulations using the direct coexistence method. In the light of this observation, we reinterpret computer simulations of ice premelting and show that current results for the TIP4P/Ice model all imply a scenario of incomplete surface melting. Using a thermodynamic integration path, we reassess our own estimates for the Laplace pressure difference between water and vapour. These calculations are used to measure the disjoining pressure of premelting liquid films and allow us to confirm a minimum of the interfacial free energy at finite premelting thickness of about one nanometer.

Davies-type phase transitions in 4D Dyonic AdS black holes from topological perspective

In this work, we discussed the Davies-type phase transitions in two distinct categories of dyonic AdS black holes (BHs). The first one is dyonic AdS BHs within four-dimensional spacetime framework. The second one is the dyonic BHs with quasitopological electromagnetism (QE) in Einstein-Gauss-Bonnet gravity (EGBG). First, we analyze the increasing and decreasing behavior of divergency depending upon different parameters which provides useful information about the region that are physical and stable. We also discuss the critical behavior of BHs in three different statistical ensembles: the canonical, mixed and grand canonical. It is noted that BHs can be classified into distinct topological classes based on their topological charge (Q) which assumes discrete values of 0,+1,−1. This topological charge plays a pivotal role in determining the phase structure and stability of the BHs within each ensemble. A topological charge of 0 corresponds to a neutral topological state that could be indicative of a more complex underlying structure, while charges of +1 or −1 indicate the presence of additional structures such as magnetic monopoles or dyons, which significantly influence the thermodynamic properties and phase transitions of the system.

Effect of dark energy on photon orbits and thermodynamic phase transition for Hayward anti-de Sitter black holes

We investigate a black hole solution analogous to Hayward regular black holes with a negative cosmological constant surrounded by quintessence — the Hayward–Kiselev anti-de Sitter (AdS) black hole, derived from Einstein equations coupled with nonlinear electrodynamics. The solution reveals a singularity due to the quintessential dark energy, and we have outlined the conditions necessary for regularity. When pressure, e.g., P=0.016, the effect of quintessential dark energy results in an otherwise absent van der Waal phase transition and second-order phase transition. Interestingly, the impact of dark energy decreases critical temperature (Tc), whereas critical pressure (Pc) increases. Investigating the correlation between photon sphere radius and the first-order phase transition exhibited non-monotonic behaviour among the photon sphere radius, nonlinear charge parameter, temperature, and pressure under certain conditions. Variations in the photon sphere radius and impact parameter before and after the phase transition serve as order parameters. The critical exponents Δrps and Δups near the critical point consistently approach 1/2, suggesting that rps and ups can be order parameters for black hole phase transitions and indicating a potential universal gravitational relationship near the critical point within a black hole thermodynamic system. We also analysed the previously unexplored Kiselev-AdS black hole, which emerges as a particular case in the limit g→0.

Thermodynamic stability versus chaos bound violation in D-dimensional RN black holes: Angular momentum effects and phase transitions

We compute the Lyapunov exponents for test particles orbiting in unstable circular trajectories around D-dimensional Reissner-Nordström (RN) black holes, scrutinizing instances of the chaos bound violation. Notably, we discover that an increase in particle angular momentum exacerbates the breach of the chaos bound. Our research centrally investigates the correlation between black hole thermodynamic phase transitions and the breaking of the chaos limit. Findings suggest that the chaos bound can only be transgressed within thermodynamically stable phases of black holes. Specifically, in the four-dimensional scenario, the critical point of the thermodynamic phase transition aligns with the threshold condition that delineates the onset of chaos bound violation. These outcomes underscore a deep-rooted link between the thermodynamic stability of black holes and the constraints imposed by the chaos bound on particle dynamics.