Narrow Results

In this paper, we investigate the quantum corrected black hole’s thermodynamic properties in this paper. To assess the local and global thermodynamic stability, we compute a number of indicators such as the geometric mass, heat capacity, Hawking temperature, thermodynamic temperature, Gibbs free energy, and energy emission. The fundamental law of thermodynamics determines the temperature of the black hole. Our results ensure the overall thermal stability of the black hole solution. Our results for Gibbs free energy and heat capacity show the phase transition behavior of the black hole.

The impact of thermal fluctuations on the thermodynamics of Born–Infeld–anti-de Sitter black hole is being investigated. For this purpose, we analyze the consequences of logarithmic corrections on thermodynamics potentials like Helmholtz and Gibbs. We find out the relations for critical points and stability and observe that thermal corrections play a vital role in them.

Among many open questions in theoretical physics, consistent quantum gravity theory is still a major issue to be solved. Recent major works in phase transitions of black holes (BH) can be helpful for quantum interpretation of classical gravity. We study the new effective method to discuss the thermodynamic phase transitions onto well renowned regular BHs. Ordinary approaches of phase transitions depend upon equation of state and it is impossible to obtain all critical points with ordinary approaches. This study is derived from the slope of temperature versus entropy and it provides the possibility of finding all the critical points analytically. This technique provides pressure, which is different from standard relation of pressure and independent of other thermodynamical relations. We discuss some issues in ordinary methods and provide an easy approach to investigate the critical behavior of thermodynamical quantities. We find out the phase transitions points and horizon radii of non-physical range for BHs. We also use the new thermodynamical relations to briefly study well-known Joule–Thomson (JT) effect on regular BH.

According to Barrow, the impact of quantum-gravitation changes the standard relation of entropy $S=\frac{A}{4}$ to $S=A^{1+\frac{\delta }{2}}$, where $A$ is actual area and $\delta$ represents the quantum-gravitational deformation effects. Keeping in mind the importance of entropy in the thermodynamics of BHs, we study the impact Barrow entropy on the thermodynamics of charged AdS BH with global monopole. We derive and plot many thermodynamical quantities of charged AdS BHs like temperature, entropy, pressure, Helmholtz free energy, Gibbs free energy, heat capacity of the system at constant pressure and volume. We study critical behavior, phase transition and thermal stability of the BH. We find out that more useful work can be extracted from the BH by using Barrow’s entropy. We also observe that Barrow entropy rapidly increases the Gibbs free energy of BH which leads to more stable behavior as compared to standard relation of entropy. We also discuss charged BH as heat engine and find out the efficiency of the BH.

This paper delves into the intriguing topic of the thermal stability of black holes (BHs) in the unique framework of bumblebee gravity. Our analysis primarily focuses on thermodynamic stability by examining the event horizon, black hole mass, thermal temperature and heat capacity. Additionally, we explore the intricacies of thermodynamic geometries such as Ruppeiner and Weinhold formulations and calculate their respective scalar curvatures in the context of bumblebee gravity. In our investigation, we also delve into the concept of phase transition through Gibbs free energy and the fascinating phenomenon of BH evaporation by energy emission. This research provides valuable insights into the complex thermodynamic properties of BHs and enhances our understanding of bumblebee gravity. We study the bosonic tunneling with spin-1 tunneling radiation in BHs. Initially, the generalized uncertainty principle (GUP) was used to correct the field equation (FE) for vector particles with spin-1 and demonstrate that the Hawking temperature rises with an improvement in the GUP and the radial component of the vector field but is unaffected by the radial components.

In this paper, the modified Hawking radiation and the P-v criticality of Reissner–Nordström-de Sitter (RNdS) black hole are investigated by using Dirac equation with Lorentz violation theory in curved space–time. Taking cosmological constant as the thermodynamic pressure and its conjugate quantity as thermodynamic volume, the analogy between the RNdS black hole in the ensemble with fixed charge and van der Waals liquid-gas system is derived. We also study the equation of state, critical exponents, critical point, heat capacity, entropy correction, Gibbs free energy. It is worth mentioning that the critical temperature, entropy, Gibbs free energy and Helmholtz free energy are modified but the critical exponents are found to be unchanged due to the influence of Lorentz violation theory. We observe that the number of Hawking–Page critical point increases due to Lorentz violation theory.

The Gibbs free energy of two highly charged plates immersed in an electrolyte solution in a finite container is investigated using mean field theory. Adiabatic potential of the charged plates, which is derived from the Gibbs free energy, has a long-range weak attractive part and medium range strong repulsive part under the Dirichlet boundary condition. From comparison with the Helmholtz adiabatic potential, it is proved that the two adiabatic potentials have qualitatively the same structure of a repulsive component and an attractive component and that the Gibbs adiabatic potential shows the stronger attractive effect.

Combining the bond-energy model and Debye theory, we generalized the Gibbs free energy model for Cu–Pt nanoparticles (NPs) by introducing a shape factor considering the shape effect. We studied the structural stability of the Cu–Pt NPs and plotted the corresponding composition-, shape- and size-dependent phase diagrams. It is shown that the Cu–Pt NPs can form alloyed structure in a large size range. But when the particle size continues to decrease, the NPs will form the core–shell structure due to surface segregation. Meanwhile, the composition segregation could make the atoms of less-content element to gather in the surface. The predictions from the present calculated phase diagrams are consistent with a series of experimental results in literatures. To further prove the efficiency of the phase diagrams, we synthesized the alloyed Cu–Pt NPs of 4–15 nm by a co-reduction method, which is in agreement with the predictions from the phase diagrams.

We studied the liquid-liquid transition in supercooled silicon modeled by the Stillinger–Weber potential. The Isothermal Isobaric Monte Carlo (NPT-MC) simulation techniques were performed here to compute the free energy difference between the two liquid phases of silicon by Bennett Acceptance Ratio (BAR) method along with a reversible path at 0.75 GPa pressure and 970 K temperature. The thermodynamic properties as energy ($\varphi$) and density ($\rho$) of the high-density liquid (HDL) phase have been computed here at different temperatures from 970–990 K. We also computed the entropy difference between the high-density liquid (HDL) and low-density liquid (LDL) phases which indicates that the glass transition temperature for the LDL phase is lower compared to the HDL phase. Further, by using the BAR method, we have computed the excess Gibbs free energy (G${}^e$) of HDL phase with respect to the crystalline phase at different temperatures in the supercooled region of SW-Silicon potential model. Based on the slope of excess Gibbs free energy with respect to temperature (T), we found that the excess entropy (S^e) of the HDL with respect to crystalline phase shows a nonmonotonic dependence on temperature at the liquid-liquid transition temperature of T${}_{\mathrm{\text{LL}}}$ = 970 K. Our results are in good agreement with the previous observation of a nonmonotonic dependence of the enthalpy on temperature in MD simulations, starting with the HDL phase at a temperature just above T${}_{\mathrm{\text{LL}}}$. All these properties are useful to understand the phase behavior of supercooled silicon and can be applicable to identify the better quality of silicon for industrial uses.

In this paper, the thermodynamics of Reissner–Nordström-anti de Sitter black hole surrounded by quintessence is studied and the impact of the Gauss–Bonnet term is measured. The modified entropy, first law of thermodynamics and corresponding Smarr relation are derived due to the combined action of the Gauss–Bonnet term and quintessence fluid. We study the so-called black hole chemistry from the analysis of the corresponding equation-of-state, conjugate potential and the critical points in the extended phase space. To study the phase transitions, we plotted $P-v$, $T-v$ and $G-T$ diagrams and analyzed the conditions for the coexistence of phases.

We study the change in internal rotational energy in the transformation of protons to neutrons in the $\beta$-decay reactions that take place in the collapse of the iron core of massive stars that precede Type II supernova explosions. We consider an ensemble of electrons, protons, neutrons and neutrinos undergoing $\beta$-decay reactions, treat the protons and neutrons as triatomic rotors, evaluate the equilibrium constant to obtain the change in rotational energy during the proton-to-neutron transformation. We estimate such change for a variety of conditions, and compare with the energy released in a supernova explosion.

Low energy isomers of and Au₄ were reexamined using the hybrid density functional B3LYP method and the couple-cluster method with the aug-cc-pVDZ-PP and aug-cc-pVTZ-PP basis sets. For , the B3LYP method favors the zigzag isomer and the second order Moller–Plesset perturbation (MP2) total energy calculation favors the D_2h rhombus isomer, whereas the couple-cluster singles and doubles with perturbative triples [CCSD(T)] level of theory favors the Y-shaped C_2v isomer. The pyramid isomer is much higher in energy and could be easily excluded. The Gibbs free energy correction based on harmonic approximation suggests that the zigzag isomer is lower in free energy than the D_2h rhombus isomer at 298.15 K. These results confirm that the Y-shaped C_2v isomer is the global minimum at both 0 K and room temperature and is thus the major isomer to account for the experimental photoelectron spectrum. The zigzag isomer is suggested, as a minor isomer, to account for the weak second peak at 3.40 eV in the experimental photoelectron spectrum. For neutral Au₄, the zigzag isomer is more stable than D_2h rhombus isomer at the B3LYP level and the D_2h rhombus isomer is the global minimum on basis of all post Hartree–Fock levels of theory.

The interaction of water soluble meso-tetra-(4N-oxyethylpyridyl) porphyrin (TOEPyP4) and its Cu(II)- and Co(II)-containing derivatives (CuTOEPyP4 and CoTOEPyP4) with A and B forms of DNA at low ionic strength was studied via UV-vis spectrophotometry and Circular Dichroism. It is shown that the binding constant of TOEPyP4 and CuTOEPyP4 with A–DNA is two times larger than with B–DNA, and the binding constant of CoTOEPyP4 does not depend on the form of DNA. The thermodynamical analysis based on spectral data indicates the preferable entropic character of porphyrins binding with both forms of DNA. This result shows that at low ionic strength the external groove binding mode is a preferred binding mechanism of these porphyrins with both forms of DNA.

When a concentrated salt solution and a diluted salt solution are separated by an ion-selective membrane, cations and anions would diffuse at different rates depending on the ion selectivity of the membrane. The difference of positive and negative charges at both ends of the membrane would produce a potential, called the diffusion potential. Thus, electrical energy can be converted from the diffusion potential through reverse electrodialysis. This study demonstrated the fabrication of an energy conversion microchip using the standard micro-electromechanical technique, and utilizing Nafion junction as connecting membrane, which was fabricated by a surface patterned process. Through different salinity gradient of potassium chloride solutions, we experimentally investigated the diffusion potential and power generation from the microchip, and the highest value measured was 135 mV and 339 pW, respectively. Furthermore, when the electrolyte was in pH value of 3.8, 5.6, 10.3, the system exhibited best performance at pH value of 10.3; whereas, pH value of 3.8 yielded the worst.

A strong understanding of the basic knowledge will help the readers not only in easily comprehending the subsequent chapters but also in grasping the analysis strategies of the latest research. In this chapter, we first introduce the elementary knowledge of electrochemical water splitting and the reaction mechanisms of hydrogen and oxygen evolution reactions, and then summarize the basic components of the test devices and crucial parameters for performance evaluation. Hopefully, this chapter can be a stepping stone for readers to comprehend the following chapters.

In the context of Chemical Engineering, thermodynamics of phase equilibrium in reactive systems is an important topic due to the growing interest in the design, synthesis and optimization of a wide variety of chemical processing operations and technologies. For reactive systems, several thermodynamic calculations can be formulated as constrained or unconstrained optimization problems. Some examples of them are phase stability and equilibriumproblems, parameter estimation in thermodynamic models, calculation of critical points, among others. Generally, these problems are non-linear, multivariable and the objective function used as the optimization criterion is non-convex even for simple reactive systems. Hence, their solution using local optimization methods is not reliable, and these thermodynamic problems are good for assessing stochastic optimization methods. This chapter^† describes the application and testing of differential evolution (DE) and tabu search (TS) methods for phase stability analysis and Gibbs energy minimization in multi-component reactive mixtures using different thermodynamicmodels.We combine the stochastic methods with a variable transformation approach to offer a reliable thermodynamic framework to model the phase equilibrium behavior of reactive mixtures. Results show that DE is better than TS for the applications tested, but requires more computational effort.