Thermodynamic Definition Research Articles

Thermodynamic formulation of vacuum energy density in flat spacetime and potential implications for the cosmological constant

We propose a thermodynamical definition of the vacuum energy density ρvac, defined as 〈vac|Tμν|vac〉 = − ρvacgμν, in quantum field theory in flat Minkowski space in D spacetime dimensions, which can be computed in the limit of high temperature, namely in the limit β = 1/T → 0. It takes the form ρvac = const ∙ mD where m is a fundamental mass scale and “const” is a computable constant which can be positive or negative depending on interaction couplings. Due to modular invariance ρvac can also be computed in a different non-thermodynamic channel where one spatial dimension is compactifed on a circle of circumference β and we confirm this modularity for free massive theories for both bosons and fermions for D = 2, 3, 4. We list various properties of ρvac that are generally required, for instance ρvac = 0 for conformal field theories, and others, such as the constraint that ρvac has opposite signs for free bosons verses fermions of the same mass, which is related to constraints from supersymmetry. Using the Thermodynamic Bethe Ansatz we compute ρvac exactly for 2 classes of integrable QFT’s in 2D and interpreting some previously known results. We apply our definition of ρvac to Lattice QCD data with two light quarks (up and down) and one additional massive flavor (the strange quark), and find it is negative, ρvac ≈ − (200 MeV)4. Finally we make some remarks on the Cosmological Constant Problem since ρvac is central to any discussion of it.

Strategies for High-Accuracy Measurements of Stage Efficiency for a Cooled Turbine

Abstract Gas turbines are used in a broad range of aerospace and land-based applications from power generation to aviation, and their usage is projected to continue to grow. It is therefore critical to improve turbine efficiency thereby reducing fuel consumption and carbon emissions. Demonstration of new efficiency-increasing technologies requires efficiency measurements that are accurate and repeatable. The Steady Thermal Aero Research Turbine (START) Laboratory at the Pennsylvania State University uses a unique 360-deg traversing system for temperature and pressure probes with redundant torque measurements to quantify thermal efficiency for a single-stage cooled test turbine. Flows in the full annulus have been analyzed and compared with subsector traverse segments centered at different circumferential positions to determine the appropriate sector size. The results from this investigation indicate that the full 360-deg measurement is recommended to minimize variation in calculated stage efficiencies. This study also compares the circumferential variations in thermodynamic and mechanical efficiency definitions, finding that the thermodynamic efficiency calculation results in a higher accuracy for full exit plane measurements. A statistical analysis was then performed to determine the number of 360-deg traverse measurements required to achieve a precision uncertainty at most that of the bias uncertainty. This study establishes guidelines to streamline experimental procedures by limiting the necessary test count per day per operating condition to five measurements for at most four test days. Following these procedures establishes a bias of ɛb = 0.19 points, resulting in a total uncertainty of at most ɛt = 0.32 points.

A possible thermodynamic definition and equation of state for a model of political election cycles.

This work demonstrates how a simulation of political discourse can be formulated using variables of the agents' behaviors in a simulation, as thermodynamic variables. With these relations the methodology provides an approach to create a correspondence between the variables of an agent based social system and those of a thermodynamic system. Extended from this observation, diagrams akin to a P-V diagram for gases can be created for this social system. The basic thermodynamic variables of temperature, pressure and volume are defined from a system of agents with political and non-political actions engaged in simulated political discourse. An equation of state is defined for the simulated political phenomenon. Through this equation of state the full thermodynamic map of the system is presented under a P-V diagram with isothermal and isentropic lines, which is able to represent the political situation of the system at each point of time. The classic election cycle that takes place can be represented on this thermodynamic map (corresponding to an Otto cycle). This provides a possibility for researching macroscopic social cycles as a thermodynamic/informational cycle as the traces on the thermodynamic map show similarities to an Otto cycle. Such a formulation reinforces the endeavours of social physics to view social phenomena with physical principles.

Quantifying ionization in hot dense plasmas.

Ionization is a problematic quantity in that it does not have a well-defined thermodynamic definition and yet it is a key parameter within plasma modeling. One still therefore aims to find a consistent and unambiguous definition for the ionization state. Within this context we present finite-temperature density functional theory calculations of the ionization state of carbon in CH plasmas using two potential definitions: one based on counting the number of continuum electrons, and another based on the optical conductivity. Differences of up to 10% are observed between the two methods. However, including "Pauli forbidden" transitions in the conductivity reproduces the counting definition, suggesting such transitions are important to evaluate the ionization state.

Thermodynamic definition of mean temperature

Thermodynamic definition of mean temperature

Tan's Two-Body Contact in a Planar Bose Gas: Experiment versus Theory.

We determine the two-body contact in a planar Bose gas confined by a transverse harmonic potential, using the nonperturbative functional renormalization group. We use the three-dimensional thermodynamic definition of the contact where the latter is related to the derivation of the pressure of the quasi-two-dimensional system with respect to the three-dimensional scattering length of the bosons. Without any free parameter, we find a remarkable agreement with the experimental data of Zou etal. [Tan's two-body contact across the superfluid transition of a planar Bose gas, Nat. Commun. 12, 760 (2021).NCAOBW2041-172310.1038/s41467-020-20647-6] from low to high temperatures, including the vicinity of the Berezinskii-Kosterlitz-Thouless transition. We also show that the short-distance behavior of the pair distribution function and the high-momentum behavior of the momentum distribution are determined by two contacts: the three-dimensional contact for length scales smaller than the characteristic length ℓ_{z}=sqrt[ℏ/mω_{z}] of the harmonic potential and, for length scales larger than ℓ_{z}, an effective two-dimensional contact, related to the three-dimensional one by a geometric factor depending on ℓ_{z}.

Prevalence and mechanism of synergistic carboxylate-cation-water interactions in halophilic proteins

The cytoplasmic proteins of some halophilic organisms remain stable and functional at multimolar concentrations of KCl, i.e., under conditions that most mesophilic proteins cannot withstand. Their stability arises from their unusual amino acid composition. The most dramatic difference between halophilic and mesophilic proteins is that the former are rich in acidic amino acids. It has been proposed that one of the evolutionary driving forces for this difference is the occurrence of synergistic interactions between multiple acidic amino acids at the surface of the protein, the potassium cations in solution, and water. We investigate this possibility with molecular dynamics simulations, using high-quality force fields for the protein-water, protein-ion, and ion-ion interactions. We create a rigorous thermodynamic definition of interactions between acidic amino acids on proteins that can be used to distinguish between synergistic, noninteracting and interfering interactions. Our results demonstrate that synergistic interactions between neighboring acidic amino acids in halophilic proteins are frequent at multimolar KCl concentration. Synergistic interactions have an electrostatic origin, and are associated with stronger water-to-carboxylate hydrogen bonds than for acidic amino acids without synergistic interactions. Synergistic interactions are not observed in minimal systems of carboxylates, indicating that the protein environment is critical for their emergence. Our results demonstrate that synergistic interactions are neither associated with rigid amino acid orientations nor with highly structured and slow moving water networks, as had been originally proposed. Moreover, synergistic interactions can also be found in unfolded protein conformations. However, because these conformations are only a small subset of the unfolded state ensemble, synergistic interactions should contribute to the net stabilization of the folded state.

From a microscopic inertial active matter model to the Schrödinger equation

Active field theories, such as the paradigmatic model known as ‘active model B+’, are simple yet very powerful tools for describing phenomena such as motility-induced phase separation. No comparable theory has been derived yet for the underdamped case. In this work, we introduce active model I+, an extension of active model B+ to particles with inertia. The governing equations of active model I+ are systematically derived from the microscopic Langevin equations. We show that, for underdamped active particles, thermodynamic and mechanical definitions of the velocity field no longer coincide and that the density-dependent swimming speed plays the role of an effective viscosity. Moreover, active model I+ contains an analog of the Schrödinger equation in Madelung form as a limiting case, allowing one to find analoga of the quantum-mechanical tunnel effect and of fuzzy dark matter in active fluids. We investigate the active tunnel effect analytically and via numerical continuation.

Determining Brown's Characteristic Curves Using Molecular Simulation.

Brown's characteristic curves define lines on the thermodynamic surface where special thermodynamic conditions hold. These curves are an important tool for the development of thermodynamic models of fluids. Yet, practically no experimental data for Brown's characteristic curves is available. In this work, a rigorous and generalized method for determining Brown's characteristic curves based on molecular simulation was developed. As multiple thermodynamic equivalent definitions apply for the characteristic curves, different simulation routes were compared. Based on this systematic approach, the most favorable route for determining each characteristic curve was identified. The computational procedure developed in this work combines molecular simulation, molecular-based equation of state, and the evaluation of the second virial coefficient. The new method was tested on a simple model system (the classical Lennard-Jones fluid) and different types of real substances (toluene, methane, ethane, propane, and ethanol). It is thereby shown that the method is robust and yields accurate results. Moreover, a computer code implementation of the method is presented.

Approach to nonlinearity parameter in liquids calculation based on the scaling theory of thermodynamic fluctuations

The nonlinearity parameter B/A is a characteristic of liquids and soft matter, which gains growing attention due to its sensibility to the composition of materials. This makes it a prospective indicator for nondestructive testing applications based on the ultrasound sounding suitable for a variety of applications from physic chemistry to biomedical studies. At the same time, the thermodynamic definition of the nonlinearity parameter requires extensive measurements at elevated pressures that are not always available; in addition, there are known certain contradiction of such data with the data obtained by methods of nonlinear acoustics. Objective. In this work, we consider a recently proposed approach to the prediction of the speed of sound at high pressures, which uses the property of invariance of the reduced pressure fluctuations and the data obtained at normal ambient pressure only. The method generalises the classic Nomoto model, which however gives only a qualitative picture, and results in the quantitative correspondence to the experimental values within their range of uncertainty. Methods. Analytical methods of the theory of thermodynamic fluctuations applied to the parameters of equations of nonlinear acoustics as well as numerical simulation in the COMSOL Multiphysics® environment. Results. Expressions for calculating the nonlinearity parameter with acceptable accuracy were obtained using thermodynamic data obtained only at atmospheric pressure. Numerical calculations were performed for toluene. In addition, the discrepancy between values of the nonlinear parameter obtained via the thermodynamic and nonlinear acoustic routes is analysed based on the numerical solution of the Westervelt equation; it is revealed that this deviation emerges when the effects of absorption of finite-amplitude waves were not properly taken into account.

Ab initio calculations of third-order elastic coefficients

Third-order elasticity (TOE) theory predicts strain-induced changes in second-order elastic coefficients (SOECs) and can model elastic wave propagation in stressed media. Although third-order elastic tensors have been determined based on first principles in previous studies, their current definition is based on an expansion of thermodynamic energy in terms of the Lagrangian strain near the natural, or zero pressure, reference state. This definition is inconvenient for predictions of SOECs under significant initial stresses. Therefore, when TOE theory is necessary to study the strain dependence of elasticity, the seismological community has resorted to an empirical version of the theory. This study reviews the thermodynamic definition of the third-order elastic tensor and proposes using an ``effective'' third-order elastic tensor. An explicit expression for the effective third-order elastic tensor is given and verified. We extend the ab initio approach to calculate third-order elastic tensors under finite pressure and apply it to two cubic systems, namely, NaCl and MgO. As applications and validations, we evaluate (a) strain-induced changes in SOECs and (b) pressure derivatives of SOECs based on ab initio calculations. Good agreement between third-order elasticity-based predictions and numerically calculated values confirms the validity of our theory.

Numerical Analysis of the Thermodynamic Definition of the Surface Tension of a Vapor–Liquid System in the Lattice Gas Model

Numerical Analysis of the Thermodynamic Definition of the Surface Tension of a Vapor–Liquid System in the Lattice Gas Model

Aspects of entropy in classical and in quantum physics

Entropy has played an essential role in the history of physics. Its mathematical definition and applications have changed over time till today. In this paper, we first review the historical evolution of these various points of view, from the thermodynamic definition to information entropy from Shannon in classical physics, up to the modern concept of Neumann’s quantum entropy. As a specific example, we consider entanglement entropy and compare the phase space approach in classical physics to the Hilbert space approach in quantum physics in simple model systems. We derive a general expression for the entanglement entropy of fermions and bosons in arbitrary partitions of Hilbert space, valid beyond the thermodynamic limit. Next, we compare thermodynamic heat engines with quantum heat engines. Finally, we proceed to the more general concept of quantum (computational) complexity and argue, using the concept of entanglement entropy, that the Heisenberg time in classically chaotic systems coincides with the time when maximal complexity is reached in the quantum case for systems with all–all interactions.

Effects of mixing and molecular packing on the isobaric expansivity of mixtures of n-hexane and 1-hexanol as modelled by FT-EoS, PC-SAFT and SAFT-[formula omitted] Mie

The behaviour of the isobaric coefficient of thermal expansion in liquids under high pressures is known as a long-standing challenge for equations of state especially with respect to the prediction of the isotherms’ crossing detected for this derivative thermodynamic quantity. Being based on a kind of universality revealed recently as relating the location of the crossing curve and the molecular packing fraction for pure non-polar liquids, here we explore more complicated situation of mixtures of a polar and a non-polar compound using prototypic compounds as an example. It is demonstrated that the Fluctuation Theory-based equation of State (FT-EoS), which uses the data along the ambient pressure conditions as a reference, has advantages in the predictive ability over the considered SAFT models and proposed a new approach connecting the parameters of the FT-EoS and the spinodal representation of the isobaric expansivity. At the same time, all three approaches argue in favour of the thermodynamic definition of the free volume that allows a microscopic interpretation of inputs of free space gaps and polar associations in the free volume and the packing fraction of complex mixtures.

Protein stability [determination] problems.

Human health depends on the correct folding of proteins, for misfolding and aggregation lead to diseases. An unfolded (denatured) protein can refold to its original folded state. How does this occur is known as the protein folding problem. One of several related questions to this problem is that how much more stable is the folded state than the unfolded state. There are several measures of protein stability. In this article, protein stability is given a thermodynamic definition and is measured by Gibbs free energy change () associated with the equilibrium, native (N) conformation ↔ denatured (D) conformation under the physiological condition usually taken as dilute buffer (or water) at 25 °C. We show that this thermodynamic quantity (), where subscript D represents transition between N and D states, and superscript 0 (zero) represents the fact that the transition occurs in the absence of denaturant, can be neither measured nor predicted under physiological conditions. However, can be measured in the presence of strong chemical denaturants such as guanidinium chloride and urea which are shown to destroy all noncovalent interactions responsible for maintaining the folded structure. A problem with this measurement is that the estimate of comes from the analysis of the plot of versus denaturant concentration, which requires a long extrapolation of values of , and all the three methods of extrapolation give three different values of for a protein. Thus, our confidence in the authentic value of is eroded. Another problem with this in vitro measurement of is that it is done on the pure protein sample in dilute buffer which is a very large extrapolation of the in vivo conditions, for the crowding effect on protein stability is ignored.

Thermodynamic Definition of Time: Considerations on the EPR Paradox

Causality is the relationship between causes and effects. Following Relativity, any cause of an event must always be in the past light cone of the event itself, but causes and effects must always be related to some interactions. In this paper, causality is developed as a consequence of the analysis of the Einstein, Podolsky, and Rosen paradox. Causality is interpreted as the result of time generation, due to irreversible interactions of real systems among them. Time results as a consequence of irreversibility; so, any state function of a system in its space cone, when affected by an interaction with an observer, moves into a light cone or within it, with the consequence that any cause must precede its effect in a common light cone.

Simulation of the carbon dioxide hydrate-water interfacial energy

HypothesisCarbon dioxide hydrates are ice-like nonstoichiometric inclusion solid compounds with importance to global climate change, and gas transportation and storage. The thermodynamic and kinetic mechanisms that control carbon dioxide nucleation critically depend on hydrate-water interfacial free energy. Only two independent indirect experiments are available in the literature. Interfacial energies show large uncertainties due to the conditions at which experiments are performed. Under these circumstances, we hypothesize that accurate molecular models for water and carbon dioxide combined with computer simulation tools can offer an alternative but complementary way to estimate interfacial energies at coexistence conditions from a molecular perspective. CalculationsWe have evaluated the interfacial free energy of carbon dioxide hydrates at coexistence conditions (three-phase equilibrium or dissociation line) implementing advanced computational methodologies, including the novel Mold Integration methodology. Our calculations are based on the definition of the interfacial free energy, standard statistical thermodynamic techniques, and the use of the most reliable and used molecular models for water (TIP4P/Ice) and carbon dioxide (TraPPE) available in the literature. FindingsWe find that simulations provide an interfacial energy value, at coexistence conditions, consistent with the experiments from its thermodynamic definition. Our calculations are reliable since are based on the use of two molecular models that accurately predict: (1) The ice-water interfacial free energy; and (2) the dissociation line of carbon dioxide hydrates. Computer simulation predictions provide alternative but reliable estimates of the carbon dioxide interfacial energy. Our pioneering work demonstrates that is possible to predict interfacial energies of hydrates from a truly computational molecular perspective and opens a new door to the determination of free energies of hydrates.

Landau theory of ferroelastic phase transitions: Application to martensitic phase transformations

The peculiarities of two Landau-type theories of ferroelastic phase transitions have been analyzed. The predictions of both theories have been compared with well-known experimental data obtained for the shape memory alloys (SMAs) undergoing the first-order martensitic transformations (MTs). It has been shown that the predictions of the Landau–Devonshire theory, which disregards the third-order term in power expansion of Gibbs free energy, contradict the experimental data, while the results of the symmetry conforming Landau theory, which takes into account this term, are in agreement with experimental data. The impossibility of occurrence of the second-order MT is demonstrated starting from the thermodynamic definition of the second-order phase transition. It is argued that the stress–strain loops, obtained for SMAs, can imitate the stress-induced phase transition in the absence of such transition.

Thermodynamic Definitions of Temperature and Kappa and Introduction of the Entropy Defect.

This paper develops explicit and consistent definitions of the independent thermodynamic properties of temperature and the kappa index within the framework of nonextensive statistical mechanics and shows their connection with the formalism of kappa distributions. By defining the “entropy defect” in the composition of a system, we show how the nonextensive entropy of systems with correlations differs from the sum of the entropies of their constituents of these systems. A system is composed extensively when its elementary subsystems are independent, interacting with no correlations; this leads to an extensive system entropy, which is simply the sum of the subsystem entropies. In contrast, a system is composed nonextensively when its elementary subsystems are connected through long-range interactions that produce correlations. This leads to an entropy defect that quantifies the missing entropy, analogous to the mass defect that quantifies the mass (energy) associated with assembling subatomic particles. We develop thermodynamic definitions of kappa and temperature that connect with the corresponding kinetic definitions originated from kappa distributions. Finally, we show that the entropy of a system, composed by a number of subsystems with correlations, is determined using both discrete and continuous descriptions, and find: (i) the resulted entropic form expressed in terms of thermodynamic parameters; (ii) an optimal relationship between kappa and temperature; and (iii) the correlation coefficient to be inversely proportional to the temperature logarithm.

Joule–Thomson expansion of RN-AdS black hole immersed in perfect fluid dark matter

In this paper, we study the Joule–Thomson expansion for RN-AdS black holes immersed in perfect fluid dark matter. As perfect fluid dark matter is one of the dark matter candidates, we are interested in how it influences the thermodynamic properties of black holes. Firstly, the negative cosmological constant could be interpreted as thermodynamic pressure and its conjugate quantity as the thermodynamic volume, which give us more physical insights into the black hole. Moreover, we derive the thermodynamic definitions and study the critical behaviour of the black hole. Secondly, the explicit expression of Joule–Thomson coefficient is obtained from the basic formulas of the pressure, the volume, the entropy and the temperature. Then, we obtain the inversion curves in terms of charge Q and parameter λ. Furthermore, we analyse the isenthalpic curve in T–P graph with the cooling–heating region determined by the inversion curve. At last, we derive the ratio of minimum inversion temperature to critical temperature and compare the result with that in the RN-AdS case.