thermodynamic potentials
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Abstract We study the thermodynamic equilibrium spectra of the Charney- Hasegawa-Mima (CHM) equation in its weakly nonlinear limit. In this limit, the equation has three adiabatic invariants, in contrast to the two invariants of the 2D Euler or Gross-Pitaevskii equations, which are examples for comparison. We explore how the third invariant considerably enriches the variety of equilibrium spectra that the CHM system can access. In particular we characterise the singular limits of these spectra in which condensates occur, i.e. a single Fourier mode (or pair of modes) accumulate(s) a macroscopic fraction of the total invariants. We show that these equilibrium condensates provide a simple explanation for the characteristic structures observed in CHM systems of finite size: highly anisotropic zonal flows, large-scale isotropic vortices, and vortices at small scale. We show how these condensates are associated with combinations of negative thermodynamic potentials (e.g. temperature).

Dynamically crosslinked gels are appealing materials for applications that require time-dependent mechanical responses. DNA duplexes are ideal crosslinkers for building such gels because of their excellent sequence addressability and flexible tunability in bond energy. However, the mechanical responses of most DNA gels are complicated and unpredictable despite the high potential of DNA. Here, we demonstrate a DNA gel with a highly homogeneous gel network and well-predictable mechanical behaviors by using a pair of star-polymer-DNA precursors with presimulated DNA sequences showing the two-state transition. The melting curve analysis of the DNA gels reveals the good correspondence between the thermodynamic potentials of the DNA crosslinkers and the presimulated values by DNA calculators. Stress-relaxation tests and dissociation kinetics measurements show that the macroscopic relaxation time of the DNA gels is approximately equal to the lifetime of the DNA crosslinkers over four orders of magnitude from 0.1-2,000 sec. Furthermore, a series of durability tests find the DNA gels are hysteresis-less and self-healable after the applications of repeated temperature and mechanical stimuli. These results demonstrate the great potential of star-polymer-DNA precursors for building gels with predictable and tunable viscoelastic properties, suitable for applications such as stress-response extracellular matrices, injectable solids, and soft robotics.

The calculation of derivatives is ubiquitous in science and engineering. In thermodynamics, in particular, state properties can be expressed as derivatives of thermodynamic potentials. The manual differentiation of complex models can be tedious and error-prone. In this work, we revisit dual and hyper-dual numbers for the calculation of exact derivatives and show generalizations to higher order derivatives and derivatives with respect to vector quantities. The methods described in this paper are accompanied by an open source Rust implementation with Python bindings. Applications of the generalized (hyper-) dual numbers are given in the context of equation of state modeling and the calculation of critical points.

The physical quality of the soil is determined by its interfacial interactions in conditions of variable water content. In this regard, water retention characteristics in the form of functions of water content and its thermodynamic potentials are used as indicators of physical quality and its dynamics in the soil. The combination of centrifugation and thermodesorption methods allowed for the first time the assessment of soil water potentials in the entire range of variation from 0 to 106 J/kg for a representative database (more than 400 samples) of the main genetic types of Eurasian soils, grouped into 5 FAO/USDA soil texture classes. The main fundamental achievement of the research is a physically based diagnosis of the critical values of water content and its thermodynamic potentials that separate the areas of dominance of various forms of soil water, physical forces, and mechanisms of interfacial interactions on the WRC-diagrams of the physical quality of the soil. Theoretical and experimental results of the study are of practical interest of sustainable agronomy for determining the optimal ranges of water content in the soil during plant cultivation, water saving, and salt protection in irrigation, mechanical tillage, and other technological operations.

In this paper, we discuss remnants of the Bardeen regular black hole motivated by using the concept of thermal fluctuations. First, we derive the equilibrium values of various thermodynamic quantities like entropy, Hawking temperature, pressure, internal energy, Helmholtz free energy and Gibbs free energy in the non-extended phase space. We then discuss geometrothermodynamics (GTD) of Bardeen black hole to study its stability. Next, we estimate the size of black hole remnant in terms of some known parameters of the black hole solution. Motivated by the fact that estimation of size, characteristics and stability of remnants of black holes could further increase our understanding of binary collisions, information loss paradox and dark energy, the black hole remnant, which gives an idea about stable mass left over after evaporation of black hole, is seen to owe its presence due to thermal fluctuations. We see that the thermal fluctuations bring an overall increase in entropy curve. However, in presence of thermal fluctuations, a positive kink, which signifies a maximum increase in the value of entropy, occurs at a certain value of horizon, which is exactly equal to the remnant radius. We observe that the thermal fluctuations, which are characteristics of quantum gravity, lead to stable values of thermodynamic quantities near the remnant radius. In presence of thermal fluctuations, we then derive various corrected thermodynamic potentials and also discuss the validity of first law of black hole thermodynamics for Bardeen black hole.

Most of the branches of engineering and basic science require,to a different extent,the use of basic thermodynamic formulas relating state variables (temperature, T; pressure, P; volume, V; entropy, S) and thermodynamic potentials (internal energy, U; Helmholtz free energy, A; enthalpy, H; Gibbs free energy, G). The different interrelations among variables, their constrains, and dependencies make them particularly difficult to remember and understand. For students learning and for chemists and engineers needing to rapidly recall these thermodynamic relationships for problem solving and practical applications, a quick method to easily remember them would be most welcome. Herein, Fishing with scissors mnemonic is presented. The mnemonic is seen as Sun with rays. Thermodynamic potential terms (A, G, H, U) as alphabetic doubles are aligned in sun rays regions where as state variables (T, P, S, V) are at sun body. Following a simple set of rules in this mnemonic, a large range of thermodynamic equations can be easily recalled without direction or sign difficulties present in previously reported methods.

The thermodynamic equilibrium of a two-phase system is described by the Gibbs equation, which includes state parameters. On the basis of the Gibbs equation and the combined equation of the first and second laws of thermodynamics, thermodynamic potentials are written: internal energy, enthalpy and Gibbs free energy. If the two phases are in equilibrium, then the temperatures, pressures and chemical potentials of these phases are equal to each other. Equalities express the conditions of thermal and mechanical equilibrium, as well as the condition for the absence of a driving force for the transfer of a component across the interface. For a two-phase system, the Gibbs-Duhem equation connects the volume and entropy of 1 mole of the mixture, the content of any component, expressed in mole fractions. Extraction from lupine particles with cheese whey (solid-liquid system) is considered. The driving force of the extraction process in the solid-liquid system is the difference between the concentration of the solvent at the surface of the solid C and its average concentration C0 in the bulk of the solution. The concentration at the interface is usually taken to be equal to the concentration of a saturated solution of Cn, since equilibrium is established rather quickly near the surface of a solid. Then the driving force of the process is expressed as Cn – C0. A curve for the extraction of extractives from lupine with cheese whey was plotted by superimposing low-frequency mechanical vibrations.