Geometrical Thermodynamics Research Articles

Controlling the Intrinsic Charge Carrier Properties of Two-Dimensional Monochalcogenides (GeSe).

Strong anisotropy exhibited by materials, particularly in their low-dimensional forms, is a highly intriguing characteristic. In this study, we investigate the effects of geometrical potential and thermodynamics on the electronic properties of monolayer monochalcogenide charge carriers. First, the geometrical potential is introduced in a monolayer structure. We discuss the Fermi surface topology of materials and the effects of the geometrical potential on the low energy bands of 2D group-IV monochalcogenides around the Γ-point. Then, the temperature dependence of the carrier mobility of the monolayer is discussed along with predictions for its potential applications as nanomaterials.

A comprehensive review of geometrical thermodynamics: From fluctuations to black holes

A comprehensive review of geometrical thermodynamics: From fluctuations to black holes

Ab Initio Thermodynamics Calculation of Beta Decay Rates

AbstractBeta‐decay half‐lives for the free neutron, for 6He and 8He, and for 8Li are calculated ab initio from geometrical thermodynamics arguments, independently of any quantum mechanics. Half‐lives for the decay of 8Be to two alphas and for the disintegration of the tetraneutron are also calculated. The calculated values are close to those experimentally observed.

Relating a System's Hamiltonian to Its Entropy Production Using a Complex Time Approach.

We exploit the properties of complex time to obtain an analytical relationship based on considerations of causality between the two Noether-conserved quantities of a system: its Hamiltonian and its entropy production. In natural units, when complexified, the one is simply the Wick-rotated complex conjugate of the other. A Hilbert transform relation is constructed in the formalism of quantitative geometrical thermodynamics, which enables system irreversibility to be handled analytically within a framework that unifies both the microscopic and macroscopic scales, and which also unifies the treatment of both reversibility and irreversibility as complementary parts of a single physical description. In particular, the thermodynamics of two unitary entities are considered: the alpha particle, which is absolutely stable (that is, trivially reversible with zero entropy production), and a black hole whose unconditional irreversibility is characterized by a non-zero entropy production, for which we show an alternate derivation, confirming our previous one. The thermodynamics of a canonical decaying harmonic oscillator are also considered. In this treatment, the complexification of time also enables a meaningful physical interpretation of both "imaginary time" and "imaginary energy".

How "Berry Phase" Analysis of Non-Adiabatic Non-Hermitian Systems Reflects Their Geometry.

There is currently great interest in systems represented by non-Hermitian Hamiltonians, including a wide variety of real systems that may be dissipative and whose behaviour can be represented by a "phase" parameter that characterises the way "exceptional points" (singularities of various sorts) determine the system. These systems are briefly reviewed here with an emphasis on their geometrical thermodynamics properties.

Thermodynamics: The New Theory of Everything?

Thermodynamics: The New Theory of Everything? Time is Complex. Chris Jeynes, Professorial Research Fellow (retired), University of Surrey Ion Beam Centre, ponders the reality of the Arrow of Time (the Second Law of Thermodynamics) and how it conditions the basic laws of physics, with reference to the The Loschmidt Paradox, The Second Law & quantum gravity, Quantitative Geometrical Thermodynamics (QGT), Thermodynamics of the Very Big and Thermodynamics of the Very small.

Structural and Electronic (Absorption and Fluorescence) Properties of a Stable Triplet Diphenylcarbene: A DFT Study.

A triplet diphenylcarbene, bis[3-bromo-5-(trifluoromethyl)[1,1'-biphenyl]-4-yl]methylidene (B3B), with exceptional stability was discovered by chemists from Japan's Mie University. To investigate its different quantum chemical features, a theoretical analysis was predicated on Density Functional Theory (DFT) and Time Dependent-DFT (TD-DFT) based technique. According to the findings, the singlet-triplet energy gap (ES-T), as well as HOMO-LUMO energy bandgap (EH-L), was found to be diminished when nucleophilicity (N) rose. We looked at the geometrical dimensions, molecular orbitals (MOs), electronic spectra, electrostatic potential, molecular surfaces, reactivity characteristics, and thermodynamics features of the title carbene (B3B). Its electronic spectra in different solvents were calculated using TD-DFT and Polarizable Continuum Model (PCM) framework. The estimated absorption maxima of B3B were seen between 327 and 340nm, relying on the solvents, and were attributed to the S0 → S1 transition. Estimated fluorescence spectral peaks were found around 389 and 407nm with the S1 and S0 transitions being identified. Its fluorescence/absorption intensities revealed a blue shift change when the solvent polarity was increased. The least exciting state has been discovered to be the π → π* charge-transfer (CT) phase. According to the Natural Bonding Orbital (NBO) exploration, ICT offers a significant role in chemical system destabilization. Furthermore, several hybrid features were used to determine the NLO (nonlinear optical) features (polarizability, first-order hyperpolarizability, and dipole moment). The calculated values suggest that B3B is a promising candidate for further research into nonlinear optical properties.

Halo Properties in Helium Nuclei from the Perspective of Geometrical Thermodynamics (Ann. Phys. 2/2022)

Geometrical Thermodynamics A new approach to physics, as described in article number 2100278, allows Mike Parker and co-workers to correctly calculate the sizes of the 4He, 6He, and 8He nuclei ab initio from thermodynamics, with no quantum mechanics, inputting only the size of the proton. The cover image illustrates the 8He nucleus modelled as an alpha particle with its holomorphic 4-neutron halo. Black holes and the cosmic holographic principle obeying Penrose (hyperbolic) geometry are also represented here and have closely related thermodynamics.

Halo Properties in Helium Nuclei from the Perspective of Geometrical Thermodynamics

AbstractThe nuclear matter and charge radii of the helium isotopes (A=4,6,8) are calculated by quantitative geometrical thermodynamics (QGT) taking as input the symmetry of the alpha‐particle, the very weak binding (and hence halo nature) of the heavier helium isotopes, and a characteristic length scale given by the proton size. The results follow by considering each isotope in its ground state, with QGT representing each system as a maximum entropy configuration that conforms to the Holographic Principle. This allows key geometric parameters to be determined from the number of degrees of freedom available. QGT treats 6He as a 4He core plus a concentric neutron shell comprising a holomorphic pair of neutrons, and the 8He neutron halo is treated as a holomorphic pair of holomorphic pairs. Considering that the information content of each system allows a correlation angle of 2π/3 between the holomorphic entities to be inferred, then the charge radii of the three isotopes can be calculated from the displacement of the 4He core from the center of mass. The calculations for the charge and matter radii of 4,6,8He agree closely with observed values. Similar QGT calculation of the sizes of the self‐conjugate A=4n nuclei {4He,8Be,12C,16O,20Ne,24Mg,28Si,32S,36Ar,40Ca} also agree well with experiment.

Geometrical thermodynamics and P-V criticality of charged accelerating AdS black holes

The unusual asymptotic structure of the accelerating black holes led to ambiguity in their geometric characteristics and thermodynamic behavior. Motivated by the interesting properties of such black holes and the significant role of electric charge and string tension on their structure, we study the thermodynamic behavior of these black holes by two methods and examine the changes of free parameters on the thermal behavior of the black holes. First, we investigate phase transition and thermal stability of the system through the use of heat capacity in the non-extended phase space. We examine the effects of electric charge, string tension and the cosmological constant on the phase transition and stability of the system. We also find that to have a phase transition, we have to apply some constraints on the free parameters. Then, we employ the geometrical thermodynamic (GT) method to study phase transition and compare the obtained results with those of the heat capacity. Next, we work in the extended phase space by considering the cosmological constant as a dynamical pressure and evaluate the existence of van der Waals like phase transition. We obtain critical quantities and study the effective role of electric charge and string tension on these quantities. Finally, we make use of the GT method in the extended phase space and find that the results of the GT method, heat capacity and P−V diagram lead to a consistent conclusion.

Entropic uncertainty principle, partition function and holographic principle derived from Liouville’s Theorem

An entropic version of Liouville’s Theorem is defined in terms of the conjugate variables (“hyperbolic position” and “entropic momentum”) of an entropic Hamiltonian. It is used to derive the Holographic Principle as applied to holomorphic structures that represent maximum entropy configurations. The Bekenstein-Hawking expression for black hole entropy is a consequence. Based on the entropic commutator derived from Liouville’s Theorem and the same entropic conjugate variables, an entropic Uncertainty Principle (in units of Boltzmann’s constant) isomorphic to the kinematic Uncertainty Principle (in units of Planck’s constant) is also derived. These formal developments underpin the previous treatment of Quantitative Geometrical Thermodynamics (QGT) which has established (entirely on geometric entropy grounds) the stability of the double-helix, the double logarithmic spiral, and the sphere. Since in the QGT formalism the Boltzmann and Planck constants are quanta of quantities orthogonal to each other in Minkowski spacetime, a solution of the Schrödinger Equation is demonstrated isomorphic to a probability term of an entropic Partition Function, where both are defined by path integrals obeying the stationary principle: this isomorphism represents an important symmetry of the formalism. The geometry of a holomorphic structure must also exhibit at least C2 symmetry.

Black string in massive gravity

We will analyze a black string in dRGT massive theory of gravity. Considering different approaches, we will study the critical behavior, phase transition and thermal stability for such a black string solution. We will analyze the Van der Waals behavior for this system, and observe that the Van der Waals behavior depends on mass of graviton. We will also analyze the geometrical thermodynamics of black strings using different thermodynamic metrics. It will be observed that the thermal fluctuations can modify the behavior of this system. We will explicitly analyze the effects of such fluctuations on the stability of this black string solutions. This will be done using the Hessian matrix for this system.

Numerical study of the mixing dynamics of trans- and supercritical coaxial jets

Characterization of the transcritical coaxial injectors, accounting for the geometrical features and thermodynamics nonlinearities, is of both practical and fundamental importance. In the present study, the interactions and effects of turbulent mixing and pseudo-boiling phenomena are investigated. To do this, the mixing dynamics of bi-shear jets injected under trans- and supercritical conditions has been investigated numerically using the large-eddy simulation technique. The numerical framework provides real-gas thermodynamics and transport properties, using the Peng–Robinson equation-of-state and Chung’s models, respectively. The obtained flow quantities are in good agreement with the pervious experimental and numerical results. Investigations show that formation of the highly stratified mixing layer and thermal-shield, a layer of large isobaric specific heat encompassing the transcritical jet, influences the transcritical mixing layer evolution. However, significant interactions of turbulent coherent structures and real-gas thermodynamics nonlinearities, referred to as the Turbulence-Thermodynamics Interaction (TTI), can locally destruct the thermal-shield and make alternate regions of gas-like and liquid-like fluids, appearing as finger-like structures on the jet interface. Therefore, it can be speculated that the initial stage of the mixing of a transcritical jet is controlled by the pseudo-boiling phenomenon that can produce strong TTI. Furthermore, local distortions of the thermal-shield provide opportunities for prominent activation of the baroclinic-torque and volume-dilatation, which, in turn, can facilitate the hydrodynamic instabilities. The growth of these instabilities disintegrates the transcritical jet’s core and results in shedding of dense lumps from the core. In addition, results indicate that nearly throughout the flow field, the baroclinic-torque to a great extent affects the turbulent-kinetic-energy.

Thermodynamics and Phase Transition of Topological Dilatonic Lifshitz‐Like Black Holes

AbstractIt is known that scalar‐tensor gravity models can be studied in Einstein and Jordan frames. In this paper, a model of scalar‐tensor gravity in Einstein's frame is considered to calculate the Lifshitz‐like black hole solutions with different horizon topologies. Thermodynamic properties and first order van der Waals‐like phase transition are studied, and it is found that the Lifshitz parameter affects the phase structure. In addition, thermal stability is investigated by using the behavior of heat capacity and various methods of geometrical thermodynamics.

Phase transition of a charged AdS black hole with a global monopole through geometrical thermodynamics

In order to study the phase transition through thermodynamic geometry, we consider the charged AdS black hole with global monopole. We first introduce thermodynamics of charged AdS black hole with global monopole by discussing the dependence of Hawking temperature, specific heat and P−v curve on horizon radius and monopole parameter. By implementing various thermodynamic geometry methods, for instance, Weinhold, Ruppiner, Quevedo and HPEM formulations, we derive corresponding scalar curvatures for charged AdS black hole with a global monopole. Here, we observe that, in contrast to Weinhold and Ruppeiner methods, HPEM and Quevedo formulations provide more information about the phase transition of the charged AdS black hole with a global monopole.

Phase transition and geometrical thermodynamics of energy-dependent dilatonic BTZ black holes with power-law electrodynamics

Abstract The coupled scalar, electromagnetic, and gravitational field equations of Einstein–dilaton gravity theory have been solved in a three-dimensional energy-dependent spacetime and in the presence of power-law nonlinear electrodynamics. The scalar potential is written as the linear combination of two exponential functions, and two families of three-dimensional dilatonic black hole solutions have been introduced which indicate the impacts of rainbow functions on the spacetime geometry. Through consideration of curvature scalars, it has been found that the asymptotic behavior of the solutions is neither flat nor anti-de Sitter. It has been illustrated that, with a suitable choice of parameters, the solutions can produce the two-horizon, extreme and naked singularity black holes. By calculating the black hole charge, mass, entropy, temperature, and electric potential, it has been proved that they fulfill the standard form of the first law of black hole thermodynamics. The thermodynamic stability of the black holes has been analyzed by utilizing the canonical and grand canonical ensembles and noting the signature of the black hole heat capacity and Gibbs free energy of the black holes. The points of type-1, type-2, and Hawking–Page phase transitions and the ranges at which the black holes are locally or globally stable have been determined. The geometrical thermodynamics of the black holes has been studied by use of different thermodynamic metrics, and the results of different approaches have been compared.

Nonlinearly charged AdS black hole solutions in three-dimensional massive gravity's rainbow

Two new families of nonlinearly charged and asymptotically anti-de Sitter (AdS) rainbow black holes have been introduced, as the exact solutions to the coupled electromagnetic and gravitational field equations, in massive gravity theory and in the presence of power-law nonlinear electrodynamics. The conserved and thermodynamic quantities such as black hole mass, charge, temperature, entropy and electric potential have been calculated from geometric and thermodynamic approaches. Despite the fact that some of them receive corrections from rainbow functions and nonlinear electrodynamics, it has been proved that they fulfill the first law of black hole thermodynamics. Thermal stability of the black holes has been studied by use of the canonical ensemble and geometrical thermodynamics methods, separately. Regarding the black hole heat capacity and thermodynamic Ricci scalars, the points of type-one and type-two phase transitions and the conditions under which the black holes remain locally stable have been determined. Also, global stability of the novel rainbow black holes has been investigated from the viewpoint of the grand canonical ensemble. Through calculation of Gibbs free energy of the black holes, the points of Hawking-Page phase transition and the size of the black holes which are globally stable or in the radiative phase have been determined.

Fullerene Stability by Geometrical Thermodynamics

AbstractThis work proves that stability of C60 is a geometrical property of the thermodynamics of the system: a significant methodological advance since a detailed treatment of the energetics may be avoidable. This approach may be fruitful, not only for fullerenes but also for general problems of molecular stability and in other applications of conformational chemistry. For the non‐chiral C60, C384, and the weakly‐chiral C28, C76 and C380 (of these, C380 and C384 are classed as “unspirallable”), Schlegel projections are used to show that these fullerenes can all be represented by pairs of spirals counter‐propagating in anti‐parallel (C2) symmetry. For C60, the high symmetry is used to construct an analytical approximation for the spherical double‐spirals, shown mathematically to be Maximum Entropy (MaxEnt) using the formalism of Quantitative Geometrical Thermodynamics (QGT). Therefore C60 is necessarily stable. This MaxEnt stability criterion is general, depending only on the geometry and not the kinematics of the system. The sense and degree of chirality for C76 and C380 is also quantified using a Shannon entropy‐based fragmentation metric.

Effects of energy dependent spacetime on geometrical thermodynamics and heat engine of black holes: Gravity's rainbow

Inspired by applications of gravity's rainbow in UV completion of general relativity, we investigate charged topological black holes in gravity's rainbow and show that depending on the values of different parameters, these solutions may encounter with black hole solutions with two horizons, extreme black hole (one horizon) or naked singularity (without horizon). First, we obtain black hole solutions, calculate thermodynamical quantities of the system and check the first law of thermodynamics. Then, we study the thermodynamical behavior of the system including thermal stability and phase transitions. In addition, we employ geometrical thermodynamics to probe phase transition points and limits on having physical solutions. Finally, we obtain heat engines corresponding to these black holes. The goal is to see how black holes' parameters such as topological factor and rainbow functions would affect efficiency of the heat engines.

Charged BTZ black holes in the context of massive gravity’s rainbow

BTZ black holes are excellent laboratories for studying black hole thermodynamics which is a bridge between classical general relativity and quantum nature of gravitation. In addition, three-dimensional gravity could have equipped us for exploring some of the ideas behind the two dimensional conformal field theory based on the $AdS_{3}/CFT_{2}$. Considering the significant interests in these regards, we examine charged BTZ black holes. We consider the system contains massive gravity with energy dependent spacetime to enrich the results. In order to make high curvature (energy) BTZ black holes more realistic, we modify the theory by energy dependent constants. We investigate thermodynamic properties of the solutions by calculating heat capacity and free energy. We also analyze thermal stability and study the possibility of Hawking-Page phase transition. At last, we study geometrical thermodynamics of these black holes and compare the results of various approaches.