System In Thermodynamic Equilibrium Research Articles

Phase transitions in systems of particles with only hard-core interactions

This article contains our comments and views on the status of the current understanding of phase transitions in systems in thermodynamic equilibrium with only hard-core interactions, based on our work in this area. The equation of state for the hard sphere gas in d-dimensions is discussed. The universal repulsive Lee-Yang singularity in the complex activity plane, and its relation to the directed and undirected polymer models are outlined. We also discuss orientationally disordered crystalline mesophases, and some of their models.

Dynamic interactions between alpha-synuclein and curved membrane surfaces.

Alpha-synuclein (α-syn) is an intrinsically disordered protein (IDP) that is abundant in neurons, where it is implicated in the pathogenesis of Parkinson's disease through cytosolic aggregation and formation of fibrils. In its healthy state, α-syn binds to synaptic lipid vesicles, transitioning to a membrane-inserting, α-helical structure in its N-terminal region while the C-terminal domain remains disordered in close proximity to the membrane. These types of disordered C-terminal domains have been shown to amplify the curvature sensitivity of several proteins through steric and/or electrostatic interactions with the membrane, which is essential for cellular function. However, little is known about the role of this disordered C-terminal domain in curvature sensing for α-syn. Additionally, little is known about the dynamic interactions of these types of disordered domains with membrane surfaces because traditional studies examine systems in thermodynamic equilibrium, which can take minutes to achieve. Conversely, many relevant cellular processes, such as cell signaling, occur on the order of seconds to milliseconds. Therefore, it is reasonable to infer that thermodynamic equilibrium does not fully encompass the complexities of α-syn's curvature sensing ability at physiologically relevant timescales. In this study, we utilize quantitative, in vitro microscopy and circular dichroism spectroscopy to examine both equilibrium and dynamic binding of α-syn to curved membranes. Our data suggests that the dissociation constant (Kd) and the association and dissociation rates (Kon and Koff) for α-syn depend on both membrane curvature and lipid composition. Both factors dictate steric and/or electrostatic interactions between C-terminal disordered domains and the membrane, as well as the density of lipid packing defects that are necessary for α-helical insertion. By employing novel strategies for investigating dynamic binding, this work unveils a previously unexplored and poorly understood category of biologically relevant IDP-membrane interactions.

The effect of vacancy defects on the electronic properties of β-Ga2O3

In this paper, the characteristics of oxygen vacancies (VO) and gallium vacancies (VGa) in β-Ga2O3 are studied using density functional theory. The performed relaxation analysis indicates that the relaxation of VGaⅡ increases its octahedral volume. Compared with the tetrahedron, the Ga atom of the octahedron surrounding VO is more stable. The formation energy results suggest also that VGa0 is expected to be most favorable in p-type β-Ga2O3, while VGa-3 is preferred in the n-type. The −3 charge state acts as a compensating acceptor, which reduces electron conductivity. VO+2, which acts as the compensation donor center, can easily form in p-type β-Ga2O3, while the VO0 forms readily in n-type β-Ga2O3. VGa at high density can exist in β-Ga2O3 in an oxygen-rich environment, while VO can exist under oxygen-poor conditions. The defect charge-state transition level reveals that VGa is a deep acceptor and VO is a deep donor. For VGa, the transition levels ε (0/-1), ε (-2/-1), and ε (-3/-2) can appear in the thermodynamic equilibrium system. However, for VOⅠ and VOIII, which are used as negative-U centers, only the transition level ε (2+/0) can appear in thermodynamic equilibrium. Furthermore, the calculated bandgap properties indicate that VGa is capable of introducing ferromagnetism in β-Ga2O3, while VO cannot. VGa introduces both acceptor levels and donor levels within the bandgap, which compensate each other, and they, thus, determine the acceptor characteristics of the system. The appearance of VO-introduced donor levels into the bandgap increases the overall electron concentration of the system. A Bader charge analysis shows that the vacancy defect can have a strong effect on the charge distribution of the crystal and alter the electronic characteristics of the crystal. The research results in this paper show that the electronic and magnetic properties of β-Ga2O3 can be changed significantly by introducing different types of vacancy defects with different charge states during the preparation process of the device. This can be done to meet specific performance requirements of a commercial electronic component.

Calculation of Gibbs partition function with imaginary time evolution on near-term quantum computers

The Gibbs partition function is an important quantity in describing statistical properties of a system in thermodynamic equilibrium. There are several proposals to calculate the partition functions on near-term quantum computers. However, the existing schemes require many copies of the Gibbs states to perform an extrapolation for the calculation of the partition function, which could be costly performed on the near-term quantum computers. We propose a scheme to calculate the Gibbs function with the imaginary time evolution. After preparing Gibbs states with different temperatures by using the imaginary time evolution, we measure the overlap between them on a quantum circuit, which allows us to calculate the Gibbs partition function. Our scheme requires only 2N qubits to calculate the Gibbs function of N qubits.

On numerical energy conservation for an implicit particle-in-cell method coupled with a binary Monte-Carlo algorithm for Coulomb collisions

Conventional particle-in-cell (PIC) methods suffer from enhanced numerical heating (explicit PIC) or cooling (semi-implicit PIC) when coupled with a binary Monte-Carlo algorithm for Coulomb collisions. In this work, a fully-implicit θ-PIC scheme (with adjustable time-biasing parameter 1/2≤θ≤1) is considered. The discrete change in energy of a closed system after a time step for this scheme scales with (1/2−θ)Cθ, where Cθ is a positive definite quantity that depends on the frequency spectrum of the energy in the fields. Collisions lead to additional energy in the field fluctuations associated with high-frequency light waves produced by a numerical Bremsstrahlung process, which can result in a large increase in the numerical cooling rate for θ>1/2. However, for θ=1/2, energy is exactly conserved. The energy in the field fluctuations on long time scales agrees with that calculated using the equipartition theorem for a classical system in thermodynamic equilibrium.

Complexity measures in terms of general dynamics: The information capacitance

We present a new context independent complexity measure, the information capacitance, for discrete probability distributions, which is based on entropy- and energy measures and describes the ability of a system to absorb or emit information. We compare the new complexity measure with the statistical definition of complexity given by Lopez-Ruiz, Mancini and Calbet. We apply both definitions in several systems which are described by discrete probability distributions. Namely, two systems beyond the thermodynamic equilibrium, i.e. a DNA-two state system and the logistic map, and also for magnetic systems in thermodynamic equilibrium. It is shown that the information capacitance takes into account spin fluctuations near phase transitions in magnetic systems.

Disorder-induced Anderson-like localization for bidimensional thermoelectrics optimization

Disorder-induced Anderson-like localization for bidimensional thermoelectrics optimization

Numerical simulations of dark matter haloes produce polytropic central cores when reaching thermodynamic equilibrium

ABSTRACT Self-gravitating astronomical objects often show a central plateau in the density profile (core) whose physical origin is hotly debated. Cores are theoretically expected in N-body systems of maximum entropy, however, they are not present in the canonical N-body numerical simulations of cold dark matter (CDM). Our work shows that despite this apparent contradiction between theory and numerical simulations, they are fully consistent. Simply put, cores are characteristic of systems in thermodynamic equilibrium, but thermalizing collisions are purposely suppressed in CDM simulations. When collisions are allowed, N-body numerical simulations develop cored density profiles, in perfect agreement with the theoretical expectation. We compare theory and two types of numerical simulations: (1) when DM particles are self-interacting (SIDM) with enough cross-section, then the effective two-body relaxation time-scale becomes shorter than the Hubble time resulting in cored DM haloes. The haloes thus obtained, with masses from dwarf galaxies to galaxy clusters, collapse to a single shape after normalization, and this shape agrees with the polytropic density profile theoretically expected. (2) The inner radii in canonical N-body numerical simulations are always discarded because the use of finite-mass DM particles artificially increases the two-body collision rate. We show that the discarded radii develop cores which are larger than the employed numerical softening and have polytropic shape independently of halo mass. Our work suggests that the presence of cores in simulated (or observed) density profiles can used as evidence for systems in thermodynamic equilibrium.

The effect of surface charge self-organization on gate-induced electron and hole two-dimensional systems

A model is proposed for describing the self-organization of localized charges and quantum scattering in undoped GaAs/AlGaAs structures in which a two-dimensional gas of electrons or holes is created by the corresponding gate voltage. We assume that in such a metal-dielectric-undoped semiconductor structure carrier scattering on surface charges localized at the interface between GaAs and the dielectric dominates. Proposed model considers these charges and the corresponding image charges in the metal gate as a closed system in a thermostat. The electrostatic self-organization for this system in thermodynamic equilibrium is studied numerically using the Metropolis algorithm in a wide temperature range. It is shown that, at T > 100 K, a simple formula derived from the theory of two-dimensional one-component plasma gives almost the same behavior of the structural factor at low wave numbers as the Monte Carlo calculation. The scattering times of gate-induced carriers are described by formulas in which the structural factor characterizes the frozen disorder in the given system. In these formulas, the behavior of the structural factor at small wave numbers is decisive. A calculation using these formulas with disorder corresponding to infinite T gives two to three times shorter scattering times than in the corresponding experiments. We found that the theory is consistent with experiment at a freezing point of disorder T ≈ 1000 K for a sample with a two-dimensional electron gas and T ≈ 700 K for a sample with a two-dimensional hole gas. The found values are an upper estimate of the freezing temperature in the studied structures, since the model ignores sources of disorder other than temperature.

Positive heat capacity in the microcanonical ensemble

The positivity of the heat capacity is the hallmark of thermal stability of systems in thermodynamic equilibrium. We show that this property remains valid for systems with negative derivative of energy with respect to temperature, as happens to some system described by the microcanonical ensemble. The demonstration rests on considering a trajectory on the Gibbs equilibrium surface, and its projection on the entropy-energy plane. The Gibbs equilibrium surface has the convexity property, but the projection might lack this property, leading to a negative derivative of energy with respect to temperature.

Homochiral Selection in a Non-equilibrium Process: Origin of Life

Chemistry and therefore life is a manifestation of the electromagnetic interaction which cannot distinguish rightfrom left, and all chemical reactions in the absence of an external chiral bias produce equal amounts of right and left-handed molecules. Nevertheless, the living matter is chiral biased and generally constituted of only one of the enantiomers, right handed or left handed. The origin of biochemical chirality remains an unresolved problem believed to be concurrent or an essential prerequisite to origion of life. Most hypotheses attempting to understand this issue, attribute homochiral selection to a biasing influence and presupposition that asymmentry can be begotten onlyfrom asymmetry. A system in thermodynamic equilibrium in the absence of a constant external chiral influence is indeed racemic and contain equal proportions of both enantiomers. Living systems and the origin of life itself are not equilibrium situations and could deviate from racemicity. A mathematical model ispresented to show that any enant iomeric selfreplicating molecule created in the racemic prebiotic medium can proliferate exhausting all precursor molecules of both handedness. The homo chirality of life is a continuation of this non-equilibrium process.

Topology and observables of the non-Hermitian Chern insulator

Topology plays a central role in nearly all disciplines of physics, yet its applications have so far been restricted to closed, lossless systems in thermodynamic equilibrium. Given that many physical systems are open and may include gain and loss mechanisms, there is an eminent need to reexamine topology within the context of non-Hermitian theories that describe open, lossy systems. The recent generalization of the Chern number to non-Hermitian Hamiltonians initiated this reexamination; however, there is so far no established connection between a non-Hermitian topological invariant and the quantization of an observable. In this work, we show that no such relationship exists between the Chern number of non-Hermitian bands and the quantization of the Hall conductivity. Using field theoretical techniques, we calculate the longitudinal and Hall conductivities of a non-Hermitian Hamiltonian with a finite Chern number to explicitly demonstrate the physics of a non-quantized Hall conductivity despite an invariable Chern number. These results demonstrate that the Chern number does not provide a physically meaningful classification of non-Hermitian Hamiltonians.

Reproducing micro X-ray computed tomography (microXCT) observations of air–water distribution in porous media using revised pore-morphology method

This study presents a novel and simple morphology approach to generate two-dimensional air–water distribution in porous media considering Or and Tuller’s cavitation mechanism (published in 2002). The connectedness condition for the nonwetting phase is replaced by the Laplace equation. An algorithm is developed to detect the ruptured water spaces that are incorrectly formed in the throat by the morphology approach, but cannot exist in a real thermodynamic equilibrium system. The distributions of soil moisture, water retention curve, and air–liquid interface area at different saturations predicted by this method are in a good quantitative agreement with the experimental observations on glass beads and Ottawa sand from micro X-raycomputed tomography (microXCT). Compared to Lu et al.’s Monte Carlo lattice-gas approach (published in 2010), another computational method to generate the soil moisture distribution, the proposed approach provides better results with significantly less computational power.

A geometric description of blackbody-like systems in thermodynamic equilibrium

Riemannian and contact geometry formalisms are used to study the fundamental equation of electromagnetic radiation-like systems, obeying a Stefan–Boltzmann’s-like law. The vanishing of metric determinant is used for classifying what kind of systems cannot represent a possible generalization of blackbody-like systems. In addition, thermodynamic curvature scalar R is evaluated for a thermodynamic metric, giving R = 0 , which validates the non-interaction hypothesis stating that the scalar curvature vanishes for non-interacting systems.

Modelling of bubble departure in flow boiling using equilibrium thermodynamics

To improve the closure relations employed for component-scale Computational Fluid Dynamics simulation of boiling flows, a first-principles method for predicting bubble departure diameters in flow boiling has been developed. The proposed method uses minimisation of the free energy of a system in thermodynamic equilibrium to predict the contact angle and the resistance to sliding of a vapour bubble attached to a surface in the presence of a forced liquid flow. Predictions of the new method are compared with measurements from existing experimental databases, and agreement with data is shown to be comparable or superior to that obtained with previous bubble departure models that have generally used a force-balance approach. The main advantages of the energy-based method over the previous force-based methods are that its formulation is simpler, and that the new model does not require the use of ad hoc tunable parameters to define force terms, or geometrical characteristics of the attached bubble such as its base area, which cannot be confirmed experimentally. This increases confidence in the validity of the new approach when applied outside the rather limited range of current test data on bubble departure in flow boiling.

About magnetism (review)

In this paper, the problem was considered contradictions magnetic Coulomb's law and the Bio-Savar-Laplass, and the question was raised about the physical sense of the magnetic vectors. The problem of finding the equilibrium described by the distribution of the surface and volume of stationary currents in a solid body. We analyzed the equilibrium state of a two-phase thermodynamic equilibrium system in the case of the classical theory of the two-fluid Gorter-Casimir, taking into account the magnetic field. It is expected that the results obtained in the course of research, can be used for further development of a modernized classical theory of superconductivity

Towards an understanding of dynamic phase transitions

We review the equivalencies and dissimilarities between ferromagnetic systems in thermodynamic equilibrium and those subjected to an external oscillating field. While the former undergo a thermodynamic phase transition at the Curie temperature, the latter show a dynamic phase transition at a critical period of the oscillating field. Over two decades of research have led to the conclusion that dynamic and thermodynamic phase transitions correspond to the same universality class and have analogous phase diagrams, among other similarities. Recently, the amplitude of the oscillating field driving the dynamic phase transition has emerged as a key variable, not only because it determines the value of the critical period directly and thus the speed of the critical dynamics, but also because it affects very substantially the degree of similarity in between thermodynamic and dynamic phase transitions. In particular, we discuss how low amplitudes of the oscillating field and corresponding slow critical dynamics lead to a suppression of the dynamic phase transition at surfaces and deviations from a Curie-Weiss type law at large periods. We also discuss the presence of metamagnetic anomalies in the paramagnetic dynamic phase and a severe shrinking of the critical region, which we have observed in magneto-optical Kerr effect experiments on in-plane uniaxial Co films and which we have analyzed in detail by means of mean-field calculations. At higher amplitudes of the oscillating field, and thus for faster critical dynamics, these phenomena are far less prominent and the equivalency picture between dynamic and thermodynamic phase transitions can be recovered.

Three faces of entropy for complex systems: Information, thermodynamics, and the maximum entropy principle

There are at least three distinct ways to conceptualize entropy: entropy as an extensive thermodynamic quantity of physical systems (Clausius, Boltzmann, Gibbs), entropy as a measure for information production of ergodic sources (Shannon), and entropy as a means for statistical inference on multinomial processes (Jaynes maximum entropy principle). Even though these notions represent fundamentally different concepts, the functional form of the entropy for thermodynamic systems in equilibrium, for ergodic sources in information theory, and for independent sampling processes in statistical systems, is degenerate, H(p)=-∑_{i}p_{i}logp_{i}. For many complex systems, which are typically history-dependent, nonergodic, and nonmultinomial, this is no longer the case. Here we show that for such processes, the three entropy concepts lead to different functional forms of entropy, which we will refer to as S_{EXT} for extensive entropy, S_{IT} for the source information rate in information theory, and S_{MEP} for the entropy functional that appears in the so-called maximum entropy principle, which characterizes the most likely observable distribution functions of a system. We explicitly compute these three entropy functionals for three concrete examples: for Pólya urn processes, which are simple self-reinforcing processes, for sample-space-reducing (SSR) processes, which are simple history dependent processes that are associated with power-law statistics, and finally for multinomial mixture processes.

Determination of H2S Partial Pressures and Fugacities in Flowing Streams

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 179921, “Determination of H2S Partial Pressures and Fugacities in Flowing Streams for a More-Accurate Assessment of Integrity Threat in Sour Systems,” by Christopher Harper, Kanan Taghiyev, and Peter Wilkie, Baker Hughes, and Douglas Hall, Chevron, prepared for the 2016 SPE International Oilfield Corrosion Conference and Exhibition, Aberdeen, 9–10 May. The paper has not been peer reviewed. An Excel-based tool was developed that uses cubic-equation-of-state (EOS) and thermodynamic electrolyte-chemistry modeling to assess sour-production streams from a reservoir, through production tubing, pipelines, and facilities to an export pipeline within a range of temperature and pressure conditions. The approach is need to assess the integrity risk posed to system components in the Alba field in the North Sea. Theory and Methodology To accurately determine multiphase sulfide concentrations, and therefore hydrogen sulfide (H2S) partial pressures and the resulting integrity threat in sour-production streams, it is first important to understand the pH-dependent distribution of the three species of sulfide that may be present in an aqueous solution. Many commercially available EOS software packages do not take into account aqueous pH- and speciation-driven aqueous sulfide solubility. They merely assume that the gas-phase and oil-phase H2S remains as H2S in all three phases and, as such, that the aqueous solubility is limited by the solubility of the H2S species in water. The three species of sulfide that may be present in an aqueous solution are H2S, HS−, and S2−. How much of each species is present (as a fraction) is dependent largely upon the aqueous pH. H2S is the only species of sulfide that exists in all three phases; some aqueous sulfide must speciate to H2S before H2S is found in the oil and gas phases. Therefore, in an oil-production system in thermodynamic equilibrium, with an aqueous pH of 9.5 or higher, all sulfide must be in the water phase and oil and gas phases must be completely free of H2S. However, this would be very unusual in an oil- production system or reservoir where typical aqueous pH values are much lower. At very low pH values, three-phase H2S distribution is driven by temperature and pressure alone: Increasing pressure reduces gas-phase H2S and increases oil- and water-phase H2S, whereas increasing temperature increases gas-phase H2S and reduces oil- and water-phase H2S (Fig. 1).

(Invited) Thermodynamics and Kinetics at the Solid-Solution Interface: Who Wins When?

The formation of self-assembled two dimensional structures at the solid-solution interface has long been treated as an equilibrium process. In the case of porphyrin adsorption this is seldom true with kinetics often determining the structures observed at temperatures below about 50°C. Using scanning tunneling microscopy (STM) we will demonstrate that molecular scale time evolution studies coupled with concentration variations are essential for determining the extent to which thermodynamics or kinetics control the observed surface structure. Examples will be given of system in thermodynamic equilibrium and of those where kinetics is controlling. We also will demonstrate how coadsorption of two species with very different desorption rates can produce new 2D structures. An interesting example of cooperative adsorption will also be presented.