Thermodynamic Space Research Articles

Thermodynamic topology of phantom AdS black holes in massive gravity

In this work, we explore the thermodynamic topology of phantom AdS black holes in the context of massive gravity. To this end, we evaluate these black holes in two distinct ensembles: the canonical and grand canonical ensembles (GCE). We begin by examining the topological charge linked to the critical point and confirming the existence of a conventional critical point (CP1) in the canonical ensemble (CE), this critical point has a topological charge of −1 and acts as a point of phase annihilation, this situation can only be considered within the context of the classical Einstein–Maxwell (CEM) theory (η=1), while no critical point is identified in the GCE. Furthermore, we consider black holes as a topological defect within the thermodynamic space. To gain an understanding of the local and global topological configuration of this defect, we will analyze its winding numbers, and observe that the total topological charge in the CE consistently remains at 1. When the system experiences a pressure below the critical threshold, it gives rise to the occurrence of annihilation and generation points. The value of electric potential determines whether the total topological charge in the GCE is zero or one. As a result, we detect a point of generation point or absence of generation/annihilation point. Based on our analysis, it can be inferred that ensembles significantly impact the topological class of phantom AdS black holes in massive gravity.

Thermodynamic topology of D = 4,5 Horava Lifshitz black hole in two ensembles

In this paper, we investigate the thermodynamic topology of four and five-dimensional Hořava-Lifshitz (HL) black holes within Hořava gravity. To analyze their thermodynamic topology, we treat these HL black holes as topological defects in their thermodynamic spaces and compute the winding numbers at these defects. Our study is conducted in two different ensembles: the fixed ϵ ensemble and the fixed ζ ensemble, where ϵ is a parameter of the HL black holes, and ζ is its conjugate parameter. In the fixed ϵ ensemble, we consider three different horizon types: spherical (k=+1), flat (k=0), and hyperbolic (k=−1), while in the fixed ζ ensemble, we examine two horizon types: spherical (k=+1) and hyperbolic (k=−1). For all the aforementioned cases, we study the local and global topology of these black holes and classify them into topological classes based on their topological charges. We calculate the topological number for each case. This process uncovers some novel phase diagrams that reveal a number of multiple defect curve phenomenon. Additionally, we explore how the topological charge of these black holes depends on the values of the thermodynamic parameters. Our findings indicate that the thermodynamic topology of Hořava-Lifshitz black holes in D=4,5 is significantly influenced by the type of horizon, the choice of ensemble, the values of pressure, and the parameters ϵ or ζ.

Thermodynamic Topology of Topological Black Hole in F(R)-ModMax Gravity’s Rainbow

Abstract In order to include the effect of high energy and topological parameters on black holes in $\mathrm{ F}(R)$ gravity, we consider two corrections to this gravity: energy-dependent spacetime with different topological constants, and a nonlinear electrodynamics field. In other words, we combine $\mathrm{ F}(R)$ gravity’s rainbow with ModMax nonlinear electrodynamics theory to see the effects of high energy and topological parameters on the physics of black holes. For this purpose, we first extract topological black hole solutions in $\mathrm{ F}(R)$-ModMax gravity’s rainbow. Then, by considering black holes as thermodynamic systems, we obtain thermodynamic quantities and check the first law of thermodynamics. The effect of the topological parameter on the Hawking temperature and the total mass of black holes is obvious. We also discuss the thermodynamic topology of topological black holes in $\mathrm{ F}(R)$-ModMax gravity’s rainbow using the off-shell free energy method. In this formalism, black holes are assumed to be equivalent to defects in their thermodynamic spaces. For our analysis, we consider two different types of thermodynamic ensembles. These are: fixed q ensemble and fixed $\phi$ ensemble. We take into account all the different types of curvature hypersurfaces that can be constructed in these black holes. The local and global topology of these black holes are studied by computing the topological charges at the defects in their thermodynamic spaces. Finally, in accordance with their topological charges, we classify the black holes into three topological classes with total winding numbers corresponding to $-1, 0$, and 1. We observe that the topological classes of these black holes are dependent on the value of the rainbow function, the sign of the scalar curvature, and the choice of ensembles.

Refined bounds on energy harvesting from anisotropic fluctuations.

We consider overdamped Brownian particles with two degrees of freedom (DoF) that are confined in a time-varying quadratic potential and are in simultaneous contact with heat baths of different temperatures along the respective DoF. The anisotropy in thermal fluctuations can be used to extract work by suitably manipulating the confining potential. The question of what the maximal amount of work that can be extracted is has been raised in recent work, and has been computed under the simplifying assumption that the entropy of the distribution of particles (thermodynamic states) remains constant throughout a thermodynamic cycle. Indeed, it was shown that the maximal amount of work that can be extracted amounts to solving an isoperimetric problem, where the 2-Wasserstein length traversed by thermodynamic states quantifies dissipation that can be traded off against an area integral that quantifies work drawn out of the thermal anisotropy. Here, we remove the simplifying assumption on constancy of entropy. We show that the work drawn can be computed similarly to the case where the entropy is kept constant while the dissipation can be reduced by suitably tilting the thermodynamic cycle in a thermodynamic space with one additional dimension. Optimal cycles can be locally approximated by solutions to an isoperimetric problem in a tilted lower-dimensional subspace.

Improved understanding of carbon nanotube growth via autonomous jump regression targeting of catalyst activity

Catalyst control is critical to carbon nanotube (CNT) growth and scaling their production. In supported catalyst CNT growth, the reduction of an oxidized metal catalyst enables growth, but its reduction also initiates catalyst deactivation via Ostwald ripening. Here, we conducted autonomous experiments guided by a hypothesis-driven machine learning planner based on a novel jump regression algorithm. This planning algorithm iteratively models the experimental response surface to identify discontinuities, such as those created by a material phase change, and targets further experiments to improve the fit and reduce uncertainty in its model. This approach led us to identify conditions that resulted in the greatest CNT yields as a function of the driving forces of catalyst reduction in a fraction of the time and cost of conventional experimental approaches. By varying temperature and the reducing potential of the growth atmosphere, we identified discontinuous jumps in CNT growth for two thicknesses of an iron catalyst, resulting in largest observed yields in narrow and distinct regions of thermodynamic space where we believe the reduced catalyst is in equilibrium with its oxide. At these jumps, we also observed the longest growth lifetimes and a greater degree of diameter control. We believe that conducting CNT growth at these conditions optimizes catalyst activity by inhibiting Ostwald ripening-induced deactivation, thereby keeping catalyst nanoparticles smaller and more numerous. This work establishes a thermodynamic framework for a generalized understanding of metal catalysts in CNT growth, and demonstrates the capability of iterative, hypothesis-driven autonomous experimentation to greatly accelerate materials science.

Understanding the phase stability in a multi-principal-component AlCuFeMn alloy

Method(s) that can reliably predict phase evolution across thermodynamic parameter space, especially in complex systems, are of critical significance in academia as well as in the manufacturing industry. In the present work, the phase stability in an equimolar AlCuFeMn multi-principal-component alloy (MPCA) was predicted using complementary first-principles density functional theory calculations and ab initio molecular dynamics (AIMD) simulations. The temperature evolution of completely disordered, partially ordered, and completely ordered phases was examined based on the Gibbs free energy. Configurational, electronic, vibrational, and lattice mismatch entropies were considered to compute the Gibbs free energy of the competing phases. Additionally, elemental segregation was studied using AIMD. The predicted results at 300 K align well with room-temperature experimental observations using x-ray diffraction and scanning and transmission electron microscopy on a sample prepared using commercially available pure elements. The adopted method could help in predicting plausible phases in other MPCA systems with complex phase stability.

Semiclassical thermodynamic geometry.

In this work the thermodynamic geometry (TG) of semiclassical fluids is analyzed. We present results for two models. The first one is a semiclassical hard-sphere (SCHS) fluid whose Helmholtz free energy is obtained from path-integral Monte Carlo simulations. It is found that, due to quantum contributions in the thermodynamic potential, the anomaly found in TG for the classical hard-sphere fluid related to the sign of the scalar curvature is now avoided in a considerable region of the thermodynamic space. The second model is a semiclassical square-well fluid, described by a SCHS repulsive interaction coupled with a classical attractive square-well contribution. The behavior of the semiclassical curvature scalar as a function of the thermal de Broglie wavelength λ_{B} is analyzed for several attractive-potential ranges. A description of the semiclassical R Widom lines, defined by the maxima of the curvature scalar, is also obtained and results are compared with the corresponding classical systems for different square-well ranges.

Methods to Calculate Entropy Generation.

Entropy generation, formulated by combining the first and second laws of thermodynamics with an appropriate thermodynamic potential, emerges as the difference between a phenomenological entropy function and a reversible entropy function. The phenomenological entropy function is evaluated over an irreversible path through thermodynamic state space via real-time measurements of thermodynamic states. The reversible entropy function is calculated along an ideal reversible path through the same state space. Entropy generation models for various classes of systems-thermal, externally loaded, internally reactive, open and closed-are developed via selection of suitable thermodynamic potentials. Here we simplify thermodynamic principles to specify convenient and consistently accurate system governing equations and characterization models. The formulations introduce a new and universal Phenomenological Entropy Generation (PEG) theorem. The systems and methods presented-and demonstrated on frictional wear, grease degradation, battery charging and discharging, metal fatigue and pump flow-can be used for design, analysis, and support of diagnostic monitoring and optimization.

Thermodynamic Topology of Black Holes in f(R) Gravity

Abstract In this work, we study the thermodynamic topology of a static, a charged static, and a charged rotating black hole in f(R) gravity. For charged static black holes, we work in two different ensembles: the fixed charge (q) ensemble and fixed potential (ϕ) ensemble. For charged rotating black holes, four different types of ensembles are considered: fixed (q, J), fixed (ϕ, J), fixed (q, Ω), and fixed (ϕ, Ω) ensemble, where J and Ω denote the angular momentum and the angular frequency, respectively. Using the generalized off-shell free energy method, where the black holes are treated as topological defects in their thermodynamic spaces, we investigate the local and global topologies of these black holes via the computation of winding numbers at these defects. For the static black hole we work in three models. We find that the topological charge for a static black hole is always −1 regardless of the values of the thermodynamic parameters and the choice of f(R) model. For a charged static black hole, in the fixed charge ensemble, the topological charge is found to be zero. Contrastingly, in the fixed ϕ ensemble, the topological charge is found to be −1. For charged static black holes, in both the ensembles, the topological charge is observed to be independent of the thermodynamic parameters. For charged rotating black holes, in the fixed (q, J) ensemble, the topological charge is found to be 1. In the fixed (ϕ, J) ensemble, we find the topological charge to be 1. In the case of the fixed (q, Ω) ensemble, the topological charge is 1 or 0 depending on the value of the scalar curvature (R). In the fixed (Ω, ϕ) ensemble, the topological charge is −1, 0, or 1 depending on the values of R, Ω, and ϕ. Therefore, we conclude that the thermodynamic topologies of the charged static black hole and charged rotating black hole are influenced by the choice of ensemble. In addition, the thermodynamic topology of the charged rotating black hole also depends on the thermodynamic parameters.

Predicting Ion Sequestration in Charged Polymers with the Steepest-Entropy-Ascent Quantum Thermodynamic Framework.

The steepest-entropy-ascent quantum thermodynamic framework is used to investigate the effectiveness of multi-chain polyethyleneimine-methylenephosphonic acid in sequestering rare-earth ions (Eu3+) from aqueous solutions. The framework applies a thermodynamic equation of motion to a discrete energy eigenstructure to model the binding kinetics of europium ions to reactive sites of the polymer chains. The energy eigenstructure is generated using a non-Markovian Monte Carlo model that estimates energy level degeneracies. The equation of motion is used to determine the occupation probability of each energy level, describing the unique path through thermodynamic state space by which the polymer system sequesters rare-earth ions from solution. A second Monte Carlo simulation is conducted to relate the kinetic path in state space to physical descriptors associated with the polymer, including the radius of gyration, tortuosity, and Eu-neighbor distribution functions. These descriptors are used to visualize the evolution of the polymer during the sequestration process. The fraction of sequestered Eu3+ ions depends upon the total energy of the system, with lower energy resulting in greater sequestration. The kinetics of the overall sequestration are dependent on the steepest-entropy-ascent principle used by the equation of motion to generate a unique kinetic path from an initial non-equilibrium state.

Topological interpretation of black hole phase transition in Gauss–Bonnet gravity

Phase transitions of Einstein–Gauss–Bonnet black holes are studied using Duan’s [Formula: see text]-field topological current theory, where black holes are treated as topological defects in the thermodynamic parameter space. The kinetics of thermodynamic defects are studied using Duan’s bifurcation theory. In this picture, a first-order phase transition between small/large black hole phases is interpreted as the interchange of winding numbers between the defects as a result of some action at a distance. We observe a first-order phase transition between small/large black holes for [Formula: see text] Einstein–Gauss–Bonnet theory similar to Reissner–Nordström black holes in AdS space. This implies that these black hole solutions share the same topology and phase structure. We have also studied the phase transition of neutral black holes in [Formula: see text] and found a transition between unstable small and large stable black hole phases similar to the case of neutral black holes in AdS space. Recently, it has been conjectured that black holes with similar topological structure exhibit the same thermodynamic properties. Our results strengthen the conjecture by connecting the topological nature of black holes to phase transitions.

An analytic and complete equation of state for condensed phase materials

Analytic equations of state (EOS) are intended to reproduce theoretical and experimental data in a single phase portion of the thermodynamic space. We devise a complete and thermodynamically consistent model with four distinct features: (1) a reference isotherm that remains thermodynamically stable, (2) a flexible specific heat model based on a fourth-order rational polynomial, (3) a Grüneisen parameter that depends on specific volume and temperature, and (4) pressure and internal energy functions that can be inverted analytically in temperature. The model aims to improve the accuracy of existing equations of state while remaining computationally efficient. To demonstrate its features, we include calibrations for single-crystal pentaerythritol tetranitrate (PETN), liquid nitromethane (NM), and hexagonal close-packed beryllium (Be) metal. The parameter optimization uses the specific heat capacity, Grüneisen parameter, and static compression curves obtained from density functional theory for the crystalline solids and molecular dynamics simulations for liquid NM. We also present a velocity autocorrelation function that yields accurate phonon densities of states for the EOS calibration from the molecular dynamics trajectories. Each of the three calibrations is constrained to enforce the ambient state from experimental measurements and validated against experimental Hugoniot data from multiple sources. We also include one-dimensional hydrodynamic simulations of the isentropic compression experiments for beryllium conducted at the Z facility.

Impact of barrow entropy on geometrothermodynamics of specific black holes

In this paper, we study the effect of Barrow entropy on the thermodynamic properties and geometry of specific black holes along with the nonlinear source. We investigate the mass, temperature, thermodynamic variable, and electric potential of the black hole as well. Furthermore, we examine the behavior of heat capacity to check the stability of a black hole. Geometrothermodynamics allows us to describe interactions between thermodynamics, critical points, and phase transitions by considering the geometric characteristics of the thermodynamic equilibrium space. Our analysis demonstrates that these findings are consistent with the results derived from the classical thermodynamics of black holes.

Machine-guided path sampling to discover mechanisms of molecular self-organization

Molecular self-organization driven by concerted many-body interactions produces the ordered structures that define both inanimate and living matter. Here we present an autonomous path sampling algorithm that integrates deep learning and transition path theory to discover the mechanism of molecular self-organization phenomena. The algorithm uses the outcome of newly initiated trajectories to construct, validate and—if needed—update quantitative mechanistic models. Closing the learning cycle, the models guide the sampling to enhance the sampling of rare assembly events. Symbolic regression condenses the learned mechanism into a human-interpretable form in terms of relevant physical observables. Applied to ion association in solution, gas-hydrate crystal formation, polymer folding and membrane-protein assembly, we capture the many-body solvent motions governing the assembly process, identify the variables of classical nucleation theory, uncover the folding mechanism at different levels of resolution and reveal competing assembly pathways. The mechanistic descriptions are transferable across thermodynamic states and chemical space.

Topological interpretation for phase transitions of black holes

In this work, we develop a universal picture from topology in the thermodynamic parameters space to describe first order phase transitions of black holes. By employing an off-shell internal energy, we find two types of topological defects. The first is normal, describing black holes which move with a nonzero velocity and acceleration, in a central force field. The second type of defects are exotic: they are static in the space, not describing black holes but encoding information about first order transitions. For each defect, we assign a winding number and an inertial mass. By studying neutral and charged black holes in asymptotically anti-de Sitter space, we show that first order transitions can be viewed as once or twice interchange of winding numbers between black holes and the exotic defects, through wired action at a distance. This corresponds to the usual notion: a smaller black hole grows into a larger black hole or vice versa. However, our topological analysis illustrates that the transition can also be locally interpreted as virtual collisions between black holes and the exotic defects. In this interpretation, a smaller black hole first grows into a new exotic defect whereas an original exotic defect grows into a larger black hole. All the defects simply change their positions and momentums, rather than interchanging the winding numbers. Critical point of the transition can be extracted when all the defects meet in the parameters space. Certain quantities, such as the Jacobians and the velocities of normal defects show universal behaviors near the critical point.

Compression of gaseous hydrogen into warm dense states up to 95 GPa using multishock compression technique

The thermodynamic properties of warm dense hydrogen, such as the equation of state (EOS) and sound velocity, affect our understanding of the evolution and interior structures of gas giant planets. However, for this low-$Z$ gas, obtaining the EOS and sound velocity experimentally under relevant planetary conditions is challenging because the extremely warm states are difficult to reach, characterize, and interrogate. Here, the multishock compression technique is used to generate the thermodynamic states of warm dense hydrogen. This provides a dynamic loading from shock adiabatic to quasi-isentropic compressions, covering wide pressure and density ranges of 0.02--95 GPa and $0.01--0.64 \mathrm{g}/{\mathrm{cm}}^{3}$, which enables us to determine the EOS and infer the high-pressure sound velocities of warm dense hydrogen relevant to planetary interiors. The data obtained in this way are comprehensively compared with several important theoretical models for astrophysics applications. The present experiments provide desirable principal- and off-Hugoniot states for revisiting the thermodynamic space of existing experimental data. These observations and thermodynamic states may be important in guiding future theoretical developments and constructing interior structure models for gas giant planets.

ON THE HEAT DISSIPATION FUNCTION FOR MAGNETIC RELAXATION PHENOMENA IN ANISOTROPIC MEDIA

Using the methods of classical irreversible thermodynamics with internal variables, the heat dissipation function for magnetizable ani­sotropic media, in which phenomena of magnetic relaxation occur, is derived. It is assumed that if different types of irreversible microscopic phenomena give rise to magnetic relaxation, it is possible to describe these microscopic phenomena splitting the total specific magnetization in two irreversible parts and introducing one of these partial specific magnetizations as internal variable in the thermodynamic state space. It is seen that, when the theory is linearized, the heat dissipation func­tion is due to the electric conduction, magnetic relaxation, viscous, magnetic irreversible phenomena. This is the case of complex media, where different kinds of molecules have different magnetic susceptibili­ties and relaxation times, present magnetic relaxation phenomena and contribute to the total magnetization. These situations arise in nuclear magnetic resonance in medicine and biology and in other fields of the applied sciences. Also, the heat conduction equation for these media is worked out and the special cases of anisotropic Snoek media and anisotropic De-Groot-Mazur media are treated.

Black Hole Solutions as Topological Thermodynamic Defects.

In this Letter, employing the generalized off-shell free energy, we treat black hole solutions as defects in the thermodynamic parameter space. The results show that the positive and negative winding numbers corresponding to the defects indicate the local thermodynamical stable and unstable black hole solutions, respectively. The topological number defined as the sum of the winding numbers for all the black hole branches at an arbitrary given temperature is found to be a universal number independent of the black hole parameters. Moreover, this topological number only depends on the thermodynamic asymptotic behaviors of the black hole temperature at small and large black hole limits. Different black hole systems are characterized by three classes via this topological number. This number could help us in better understanding the black hole thermodynamics and, further, shed new light on the fundamental nature of quantum gravity.

The square-well fluid: A thermodynamic geometric view

The square-well fluid with hard-sphere diameters is studied within the framework of Thermodynamic Geometry (TG). Coexistence and spinodal curves, as well as the Widom line for ranges λ∗=1.25,1.5,2.0,3.0 for this fluid are carefully studied using geometric methods. We are able to show that, unlike coexistence curves, an exact result can be given along all the thermodynamic space and for all potential ranges for spinodal curves. Additionally, R-Widom line which is defined as the locus of extrema of the curvature scalar is calculated as a function of the potential range, satisfying near the critical point a relation that bears a resemblance with the Clausius–Clapeyron equation. Besides, a brief exploration of scalar curvature criticality is also provided.

QED effects on phase transition and Ruppeiner geometry of Euler-Heisenberg-AdS black holes* *Supported by the National Natural Science Foundation of China (12075103, 11675064, 12047501) and the 111 Project (B20063)

Considering the quantum electrodynamics (QED) effect, we study the phase transition and Ruppeiner geometry of Euler-Heisenberg anti-de Sitter black holes in the extended phase space. For negative and small positive QED parameters, we observe a small/large black hole phase transition and reentrant phase transition, respectively, whereas a large positive value of the QED parameter ruins the phase transition. Phase diagrams for each case are explicitly shown. Then, we construct the Ruppeiner geometry in thermodynamic parameter space. Different features of the corresponding scalar curvature are shown for both the small/large black hole phase transition and reentrant phase transition cases. Of particular interest is the additional region of positive scalar curvature, indicating a dominant repulsive interaction among black hole microstructures, for the black hole with a small positive QED parameter. Furthermore, universal critical phenomena are observed for the scalar curvature of Ruppeiner geometry. These results indicate that the QED parameter has a crucial influence on the black hole phase transition and microstructure.