Thermodynamic Quantities Research Articles

Divergence of thermalization rates driven by the competition between finite temperature and quantum coherence

The thermalization of an isolated quantum system is described by quantum mechanics and thermodynamics, while these two subjects are still not fully consistent with each other. This leaves a less-explored region where both quantum and thermal effects cannot be neglected, and the ultracold-atom platform provides a suitable and versatile testbed to experimentally investigate these complex phenomena. Here we perform experiments based on ultracold atoms in optical lattices and observe a divergence of thermalization rates of quantum matters when the temperature approaches zero. By ramping an external parameter in the Hamiltonian, we observe the time delay between the internal relaxation and the external ramping. This provides us with a direct comparison of the thermalization rates of different quantum phases. We find that the quantum coherence and bosonic stimulation of superfluid induces the divergence while the finite temperature and the many-body interactions are suppressing the divergence. The quantum coherence and the thermal effects are competing with each other in this isolated thermal quantum system, which leads to the transition of thermalization rate from divergence to convergence.

Phantom BTZ black holes

Motivated by the impact of the phantom field (or anti-Maxwell field) on the structure of three-dimensional black holes in the presence of the cosmological constant, we present the first extraction of solutions for the phantom BTZ (A)dS black hole. In this study, we analyze the effect of the phantom field on the horizon structure. Furthermore, we compare the BTZ black holes in the presence of both the phantom and Maxwell fields. Additionally, we calculate the conserved and thermodynamic quantities of the phantom BTZ black holes, demonstrating their compliance with the first law of thermodynamics. Subsequently, we assess the effects of the electrical charge and the cosmological constant on the local stability in the canonical ensemble by considering these fields with respect to the heat capacity. We then investigate the global stability area of the BTZ black holes with phantom and Maxwell fields within the grand canonical ensemble using Gibbs free energy. In this analysis, we evaluate the influence of the electrical charge and the cosmological constant on this area.

Electrical conductance study of Schiff base in different solvents and temperatures: DFT calculation

The electrical conductivities of the N-(2-chlorobenzylidene)benzylamine (NCB) as Schiff bases (SB) compound in water and methanol were studied in different temperatures, the mixtures of methanol and water studied in various percentages of methanol at 298 K. Initially, the relationship between equivalent conductivity and the square root of molar concentration was plotted to find electrolyte types using Kohlrausch equations. The plot indicates that NCB was weakly associated with water, methanol, and mixtures. Lee-Wheaton equation treated the experimental results of symmetrical electrolytes (1:1) to calculate the conductivity confines: equivalent conductance at infinite dilution Λₒ, association constant KA, and the main distance between ions in solution (R) at best-fit values of (ϬΛ). Thermodynamic quantities for the ion association reaction (∆Go, ∆Ho and ∆So) have been measured. Also, the theoretical calculation was used to optimize the energy of the molecule in the gas phase then measured many descriptors by using (AM1, PM3) then DFT. In addition, recalculated the optimization energy in water, and methanol. After theoretical calculation and analysis, it was found that the Λₒ value is related to the molecular volume of the system (molecules assembled in the solvent). As the molecular volume increases, the Λₒ value decreases due to association. KEY WORDS: Schiff bases, Electrical conductivities, Lee-Wheaton equation, Thermodynamic parameter, DFT Bull. Chem. Soc. Ethiop. 2025, 39(1), 177-187. DOI: https://dx.doi.org/10.4314/bcse.v39i1.15

Thermodynamic study of pyridoxine in different solvents and temperatures: DFT study

The equivalent conductivities (Λ) of B6 vitamin (pyridoxine) in HշՕ and MeOH were measured at different temperatures between 293 to 313 K, as well as in mixtures of H₂O and MeOH at percentages of 10, 20, 30, 40, and, 50% MeOH at 310 K. All the practical results were mathematically processed using the Lee Wheaton equation, which is applied to the derived conductivity of electrolytes with a similar composition (1:1). This equation calculates various conductivity components, including the equivalent conductance at infinite dilution (Λₒ), the ionic conductivity, the distance between ions (R), and also the constant of ionic aggregation (Ka) at best-fit values of (ϬΛ). The values of these parameters differed from one solvent to another depending on the molecular interactions in the solution and the physical properties of the solvents, such as viscosity and dielectric constant. Finally, thermodynamic quantities for the ion association reaction (ΔG°, ΔH°, and ΔS°) were also studied. Density functional theory (DFT) calculations (B3LYP/6-31G (d,p)) were employed to analyze vitamin B6 in the gas phase and diverse solvents. Three different continuum methods, namely AM1, PM3, and HF, were utilized, followed by DFT. The final method was utilized to explore the effects on its characteristics. KEY WORDS: Electrical conductivity, Lee-Wheaton equation, Theoretical chemistry, DFT. Bull. Chem. Soc. Ethiop. 2025, 39(1), 165-176. DOI: https://dx.doi.org/10.4314/bcse.v39i1.14

New insights into the prediction for the potential of soil organic carbon accumulation: From the perspective of non-equilibrium statistical mechanics

The accumulation of soil organic carbon (SOC) is significant for soil health and ecosystem services. Numerous studies have assessed the dynamic changes of SOC by considering the microbial system as an equilibrium system. However, they failed to reveal the complexity of the SOC accumulation/loss process, as the microbial system is a non-equilibrium system affected by stochastic fluctuations from the external environment. This study is the first to explore the complex non-equilibrium relationship between microbial carbon use efficiency (CUE) and SOC by using potential landscape and flux in non-equilibrium statistical mechanics. Nitrogen (N) was identified as the most critical environmental factor influencing CUE on a global scale, with the transition between the carbon loss state and the carbon sequestration state observed along N gradients. Random perturbations of other environmental factors could also trigger transition. Non-equilibrium thermodynamic quantities indicated that carbon sequestration had the potential to be achieved when N = 0.5 g/kg, where active soil management measures should be taken. Furthermore, the non-equilibrium relationship between CUE and SOC was clarified through potential energy analysis, where the average deviation between predictions and actual observations of SOC is about 1.9792 g/kg. This study provides an effective framework for predicting SOC accumulation.

Quantum gravity phenomenology and the blackbody radiation

Abstract We analyze the blackbody radiation problem in the presence of quantum gravity effects encoded in modified dispersion relations. The spectral radiance and the generalized Stefan-Boltzmann law are studied in this context. Furthermore, the regime of low temperatures is also contemplated, where features related to the blackbody thermal laws and the thermodynamic quantities such as energy, pressure, entropy, and specific heat are obtained. Possible implications in compact objects such as neutron stars are also discussed.

Investigating zero-point vibrations of solid hydrogen via statistical moment method

Zero-point vibrations of solid hydrogen are investigated by analyzing the molecular mean-squared displacement (MSD) and mean-squared relative displacement functions within the statistical moment method approach in statistical mechanics. Numerical computations of these thermodynamic properties were conducted for solid hydrogen from 0 K to its phase transition temperature using the Wigner-Kirkwood mean-field potential derived from the Buckingham exp-6 potential. We have shown that the quantum-mechanical zero-point vibrations play an important role at low temperature. And these thermodynamic quantities increase with temperature, suggesting that both thermal and quantum effects play a significant role near the liquid-solid phase transition. The favorable consistency between our findings and the recent experimental inelastic neutron scattering measurements of MSD attests to the potential of SMM as a novel approach for determining the atomic vibrations of solid hydrogen. This approach allows us to study these effects including the anharmonicity of lattice vibrations.

Work extraction from quantum coherence in non-equilibrium environment

Ergotropy, which represents the maximum amount of work that can be extracted from a quantum system, has become a focal point of interest in the fields of quantum thermodynamics and information processing. In practical scenarios, the interaction of quantum systems with their surrounding environment is unavoidable. Recent studies have increasingly focused on analyzing open quantum systems affected by non-stationary environmental fluctuations due to their significant impact on various physical scenarios. While much research has concentrated on work extraction from these systems, it often assumes that the environmental degrees of freedom are substantial and that the environment is effectively in equilibrium. This has led us to explore work extraction from quantum systems under non-stationary environmental conditions. In this work, the dynamics of ergotropy will be investigated in a non-equilibrium environment for both Markovian and non-Markovian regime. In this study, both the coherent and incoherent parts of the ergotropy will be considered. It will be shown that for a non-equilibrium environment, the extraction of work is more efficient compared to when the environment is in equilibrium.

A comprehensive study on a tapered Paul trap: from design to potential applications

Abstract We present a tapered Paul trap whose radio frequency electrodes are inclined to the symmetric axis of the endcap electrodes, resulting in a funnel-shaped trapping potential. With this configuration, a charged particle confined in this trap has its radial degrees of freedom coupled to that of the axial direction. The same design was successfully used to experimentally realize a single-atom heat engine, and with this setup amplification of zeptonewton forces was implemented. In this paper, we show the design, implementation, and characterization of such an ion trap in detail. This system offers a high level of control over the ion’s motion. Its novel features promise applications in the field of quantum thermodynamics, quantum sensing, and quantum information.

Thermodynamically Traceable Calorimetric Results for Aqueous Sodium Chloride Solutions from T = (273.15 to 373.15) K up to the Saturated Solutions: Part 2 —The Quantities Associated with the Partial Molar Heat Capacity

AbstractIn previous articles (Partanen and Partanen in J. Chem. Eng. Data 65: 5226 − 5239 (2020), J. Solution Chem. 52: 1352 − 1385 (2023)), we presented a traceable and transparent three-parameter model for thermodynamic activity and enthalpy quantities in aqueous NaCl solutions. The model is based on extended Hückel equations with parameters B, b1, and b2 and it applies from T = 273.15 to 373.15 K up to the saturated solutions. These studies demonstrate that the model explains the literature data of almost all thermodynamic quantities including apparent and partial molar enthalpies within experimental error. In the model, the ion-size parameter in the Debye–Hückel equation, B, is regarded as a constant while the parameters of the coefficients of the linear and quadratic molality terms, b1 and b2, respectively, possess quadratic temperature dependences. In this study, the results obtained for the heat capacity quantities of NaCl(aq) are considered. We show that the available heat capacity literature for these solutions can be predicted at least satisfactorily up to the saturated solutions with our new model. Following this success, we supplement the existing thermodynamic tables with the new values for the relative apparent and partial molar heat capacities for NaCl solutions. It is likely that the new tables contain the most reliable values determined so far even though no calorimetric data were used in the parameter estimation of our model. Graphical Abstract

Restricted Phase Space Thermodynamics of NED-AdS Black Holes

Abstract We study the Restricted Phase Space Thermodynamics (RPST) of magnetically charged Anti de Sitter (AdS) black holes sourced by nonlinear electrodynamics(NED). The first law and the corresponding Euler relation are examined using the scaling properties. While the mass is homogeneous in the first order, the intensive variables are observed to follow zeroth order homogeneity. We use numerical and graphical techniques to find the critical points of the various thermodynamic quantities. By utilizing the re-scaling properties of the equation of states, we study the thermodynamic processes using different pairs of variables. From our analysis, we infer that although the RPS thermodynamics of NED-AdS black hole resembles those of RN-AdS, Kerr-AdS, Kerr-Sen-Ads black holes in most of its aspects, hinting at a possible universality, there exists one particular μ − C process that differs in its behaviour from its counterparts in earlier reported works.

Temperature dependence of the frequency shifts related to the thermodynamic quantities close to phase transitions in NaNO2

ABSTRACT This study examines a linear relationship between the frequency shifts, ( 1 / w ) ( ∂w / ∂T ) p , and the variation of the dielectric constant, ( 1 / ϵ ) ( ∂ϵ / ∂T ) p , close to phase transitions in ferroelectric crystalline systems, in particular, ferroelectric NaNO2 as studied here. Both quantities (frequency and dielectric constant) are described by the power-law formulae below the Curie temperature Tc (ferroelectric phase), Tc < T < Ti (incommensurate phase) and T > Ti (paraelectric phase). The divergence behaviour of the mode Grüneisen parameter (ɣp ) is obtained, whose temperature dependence can also be described by a power-law formula in NaNO2. It is also shown that the heat capacity Cp can be evaluated from the thermal expansion (αp ) by means of the same critical exponent since they exhibit similar critical behaviour near Tc and Ti in this crystal.

Key Issues Review: Useful autonomous quantum machines.

Controlled quantum machines have matured significantly. A natural next step is to increasingly grant them autonomy, freeing them from time-dependent external control. For example, autonomy could pare down the classical control wires that heat and decohere quantum computers; and an autonomous quantum refrigerator recently reset superconducting qubits to near their ground states, as is necessary before a computation. Which fundamental conditions are necessary for realizing useful autonomous quantum machines? Inspired by recent quantum thermodynamics and chemistry, we posit conditions analogous to DiVincenzo's criteria for quantum computing. Furthermore, we illustrate the criteria with multiple autonomous quantum machines (refrigerators, computers, clocks, etc.) and multiple candidate platforms (neutral atoms, molecules, superconducting qubits, etc.). Our criteria are intended to foment and guide the development of useful autonomous quantum machines.

Corrected Thermodynamics of Black Holes in f(R) Gravity with Electrodynamic Field and Cosmological Constant.

The thermodynamics of black holes (BHs) and their corrections have become a hot topic in the study of gravitational physics, with significant progress made in recent decades. In this paper, we study the thermodynamics and corrections of spherically symmetric BHs in models f(R)=R+αR2 and f(R)=R+2γR+8Λ under the f(R) theory, which includes the electrodynamic field and the cosmological constant. Considering thermal fluctuations around equilibrium states, we find that, for both f(R) models, the corrected entropy is meaningful in the case of a negative cosmological constant (anti-de Sitter-RN spacetime) with Λ=-1. It is shown that when the BHs' horizon radius is small, thermal fluctuations have a more significant effect on the corrected entropy. Using the corrected entropy, we derive expressions for the relevant corrected thermodynamic quantities (such as Helmholtz free energy, internal energy, Gibbs free energy, and specific heat) and calculate the effects of the correction terms. The results indicate that the corrections to Helmholtz free energy and Gibbs free energy, caused by thermal fluctuations, are remarkable for small BHs. In addition, we explore the stability of BHs using specific heat. The study reveals that the corrected BH thermodynamics exhibit locally stable for both models, and corrected systems undergo a Hawking-Page phase transition. Considering the requirement on the non-negative volume of BHs, we also investigate the constraint on the EH radius of BHs.

A Study of q-Deformed Bosons, and Their Implications to Quantum Optics

In this study, we investigate three types of q-deformed boson oscillators, focusing on their mathematical frameworks and thermodynamic properties. We calculate key thermodynamic quantities, such as internal energy and entropy, as functions of the deformation parameter q. Our results reveal that these oscillators are eigenstates of specific deformed boson annihilation operators. We also analyze their unique characteristics and implications in deformed quantum optics. Furthermore, we examine the impact of q-deformation on qutrit logic gates, including cycle, self-shift, controlled cycle, controlled self-shift, Feynman, ternary Toffoli, and Fredkin gates, highlighting their altered computational properties. This research contributes to a deeper understanding of q-deformed systems and their applications in quantum computing. Overall, it opens new avenues for exploring the interplay between deformation parameters and quantum information processing.

Muon spin relaxation study of spin dynamics on a Kitaev honeycomb material H3LiIr2O6

The vacancy effect in quantum spin liquid (QSL) has been extensively studied. A finite density of random vacancies in the Kitaev model can lead to a pileup of low-energy density of states (DOS), which is generally experimentally determined by a scaling behavior of thermodynamic or magnetization quantities. Here, we report detailed muon spin relaxation (μSR) results of H3LiIr2O6, a Kitaev QSL candidate with vacancies. The absence of magnetic order is confirmed down to 80 mK, and the spin fluctuations are found to be persistent at low temperatures. Intriguingly, the time-field scaling law of longitudinal-field (LF)-μSR polarization is observed down to 0.1 K. This indicates a dynamical scaling, whose critical exponent of 0.46 is excellently consistent with the scaling behavior of specific heat and magnetization data. All the observations point to the finite DOS with the form N(E)∼E−ν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N(E)\\sim {E}^{-\ u }$$\\end{document}, which is expected for the Kitaev QSL in the presence of vacancies. Our μSR study provides a dynamical fingerprint of the power-law low-energy DOS and introduces a crucial new insight into the vacancy effect in QSL.

Role of biquadratic exchange on thermodynamic quantities in anisotropic Heisenberg model

The magnetic and thermodynamic properties of the spin-1 anisotropic Heisenberg system are studied within Oguchi approximation. The system contains both the bilinear and biquadratic exchange interactions between the nearest neighboring spins located on a centered honeycomb lattice. For the positive biquadratic exchange interaction parameters, the phase transition in the Heisenberg case is of both second and first order where there is a discontinuity in the thermodynamic properties at this transition temperature. For some negative biquadratic exchange interaction parameters, in both the Heisenberg and Ising cases, the ferromagnetic state changes in favor of the antiferromagnetic state. The frustrated antiferromagnetic structure created by the biquadratic exchange parameter with negative sign was shown significantly influence the magnetization, quadrupolar moment, internal energy, heat capacity, entropy and free energy of the system, where the system has an oscillating chaotic phase regime. A double peak behavior was observed in the specific heat, with one at the critical temperature and another at a low temperature.

Infinite cycles of interacting bosons

Abstract In the first-quantized description of bosonic systems permutation cycles formed by the particles play a fundamental role. In the ideal Bose gas Bose-Enstein condensation (BEC) is signaled by the appearance of infinite cycles. When the particles interact, the two phenomena may not be simultaneous, the existence of infinite cycles is necessary but not sufficient for BEC. We demonstrate that their appearance is always accompanied by a singularity&amp;#xD;in the thermodynamic quantities&amp;#xD;which in three and four dimensions can be as strong as a one-sided divergence of the isothermal compressibility. Arguments are presented that long-range interactions can give rise to unexpected results, such as the absence of infinite cycles in three dimensions for long-range repulsion or their presence in one and two dimensions if the pair potential has a long attractive tail.

Extended Local Ergotropy.

A fundamental problem in quantum thermodynamics is to properly quantify the work extractable from out-of-equilibrium systems. While for closed systems, maximum quantum work extraction is defined in terms of the ergotropy functional, this question is unclear in open systems interacting with an environment. The concept of local ergotropy has been proposed, but it presents several problems, such as it is not guaranteed to be nonincreasing in time. Here, we introduce the concept of extended local ergotropy by exploiting the free evolution of the system-environment compound. At variance with the local ergotropy, the extended local ergotropy is greater, is nonincreasing in time, and activates the potential of work extraction in many cases. We then concentrate on specific schemes in which we alternate repeated local unitaries and free system-environment evolution. We provide examples based on the Jaynes-Cummings model, presenting practical protocols and analytic results that serve as proof of principle for the aforementioned advantages.

Thermodynamic and dielectric properties of hexagonal barium titanate near the phase transitions

The critical behavior of the thermodynamic quantities is studied for the two phase transitions near the transition temperatures (74 K and 222 K) in the hexagonal (h) BaTiO3. A linear relationship has been established between the variations of the frequency shifts and of the dielectric constant by using the literature data in h-BaTiO3. Temperature and pressure dependence of the mode Grüneisen parameters ( γp and γT ) are also described by a power-law formula as the other thermodynamic parameters near Tpt in h-BaTiO3. Our results show that they explain the observed behavior adequately, in particular soft-mode frequency, dielectric constant, thermal expansion, the excess specific heat and the entropy near Tpt in h-BaTiO3. Temperature dependence of the isobaric mode Grüneisen parameter ( γp ), enthalpy and the Gibbs free energy, which we have evaluated, can be compared with experiments in h-BaTiO3.