Temperature In Thermodynamics Research Articles

Thermal stability of stealth and de Sitter spacetimes in scalar-tensor gravity

Stealth solutions of scalar-tensor gravity and less-known de Sitter spaces that generalize them are analyzed regarding their possible role as thermal equilibria at non-zero temperature in the new first-order thermodynamics of scalar-tensor gravity. No stable equilibria are found, further validating the special role of general relativity as an equilibrium state in the landscape of gravity theories, seen through the lens of first-order thermodynamics.

Average Turbulence Dynamics from a One-Parameter Kinetic Theory

We show theoretically that the mean turbulent dynamics can be described by a kinetic theory representation with a single free relaxation time that depends on space and time. A proper kinetic equation is constructed from the Klimontovich-type kinetic equation for fluid elements, which satisfies the Navier–Stokes hydrodynamics exactly. In a suitably averaged form, the turbulent kinetic energy plays the role of temperature in standard molecular thermodynamics. We show that the dynamics of turbulent fluctuations resembles a collision process that asymptotically drives the mean distribution towards a Gaussian (Maxwell–Boltzmann) equilibrium form. Non-Gaussianity arises directly from non-equilibrium shear effects. The present framework overcomes the bane of most conventional turbulence models and theoretical frameworks arising from the lack of scale separation between the mean and fluctuating scales of the Navier-Stokes equation with an eddy viscous term. An averaged turbulent flow in the present framework behaves more like a flow of finite Knudsen number with finite relaxation time, and is thus more suitably described in a kinetic theory representation.

Characteristics of MgO-based sorbents for CO2 capture at elevated temperature and pressure

MgO-based sorbents are promising candidates for precombustion CO2 capture performed at elevated temperature and pressure in thermodynamics, where the development of efficient sorbents is of great importance. Herein, we report MgO-Na2CO3-KNO3 sorbents with fast sorption kinetics, high capture capacity and good cyclic stability at elevated conditions. The effects of nitrate species, Na2CO3 doping amounts and sorption conditions on the MgO conversion were investigated during cyclic test. In comparison with LiNO3 and NaNO3, the sample with KNO3 possesses the highest MgO conversion, which increases from 0.78 to 0.86 after 30 cycles with sorption at 400 °C, 2 MPa. For nitrate-promoted MgO, Na2CO3 plays an essential role in the initial fast sorption rate. The sorbent with 60 mol%Na2CO3 possesses the highest MgO conversion of 0.89 after 30 cycles. Moreover, during the operation range of 400 ℃-480 ℃, 2 MPa, the sorbent exhibits an excellent cyclic stability with porous structure. Density functional theory calculations are further conducted to investigate the mechanism of performance improvement brought by Na2CO3. We find dissolved CO32– ions will provide chemisorption sites through the formation of C(CO2)-O(CO32–) bonds and can serve as the CO2 carrier in molten nitrate salts, thus improving both sorption and diffusion rates of CO2.

Probing Hawking radiation through capacity of entanglement

We consider the capacity of entanglement in models related with the gravitational phase transitions. The capacity is labeled by the replica parameter which plays a similar role to the inverse temperature in thermodynamics. In the end of the world brane model of a radiating black hole the capacity has a peak around the Page time indicating the phase transition between replica wormhole geometries of different types of topology. Similarly, in a moving mirror model describing Hawking radiation the capacity typically shows a discontinuity when the dominant saddle switches between two phases, which can be seen as a formation of island regions. In either case we find the capacity can be an invaluable diagnostic for a black hole evaporation process.

Contribution to COVID-19 spread modelling: a physical phenomenological dissipative formalism.

In this study, we propose an evolution law of COVID-19 transmission. An infinite ordered lattice represents population. Epidemic evolution is represented by a wave-like free spread starting from a first case as an epicentre. Free energy of the virus on a given day is defined equal to the natural logarithm of active infected cases number. We postulate a form of free energy built using thermodynamics of irreversible processes in analogy to isotherm wave propagation in solids and non-local elastic damage behaviour of materials. The proposed expression of daily free energy rate leads to dissipation of propagation introducing a parameter quantifying measures taking by governments to restrict transmission. Entropy daily rate representing disorder produced in the initial system is also explicitly defined. In this context, a simple law of evolution of infected cases as function of time is given in an iterative form. The model predicts different effects on peak of infected cases Imax and epidemic period, including effects of population size N, effects of measures taking to restrict spread, effects of population density and effect of a parameter T similar to absolute temperature in thermodynamics. Different effects are presented first. The model is then applied to epidemic spread in Tunisia and compared with data registered since the report of the first confirmed case on March 2, 2020. It is shown that the low epidemic size in Tunisia is essentially due to a low population density and relatively strict restriction measures including lockdown and quarantine.

Parallel Maxwellian relations and their correlations in nonextensive thermodynamics

We presented a prescript in previous works to solve the issue of the definition of temperature in thermodynamics on the basis of the dual interpretation of temperature concept. A nonextensive thermodynamic formalism consisting of two sets of parallel Legendre transformation structures, namely, physical and Lagrange sets, were proposed by providing further dual interpretations of thermodynamic quantities. In this study, we reconstruct Maxwellian and other thermodynamic relations on the basis of these two parallel formalisms. The correlations between the thermodynamic relations are determined, where an equivalent rule is suggested, by recoursing to the link of the Tsallis factor. This rule shows that the Tsallis factor is invariable with a constant volume or entropy in partial derivative calculations. These correlations could be easily tested in nonextensive statistics, whose applications into adiabatic expansions of nonextensive gas produce interesting results. Lagrange internal energy and generalized heat capacity are negative in some small nonextensive systems due to the enhanced nonextensive effect. The negative definite of generalized heat capacity would not lead to instability, as physical heat capacity is the quantity used to govern the thermodynamic process of nonextensive systems.

A probabilistic rate theory connecting kinetics to thermodynamics

Kinetics and thermodynamics are largely disconnected in current theories because Arrhenius activation energies (Ea) have strictly no influence on equilibrium distributions. A first step towards the incorporation of rate theories in thermodynamics is the identification of the pre-exponential term of the Arrhenius equation as an entropic quantity. A second step examined here is the possible contribution of Ea in equilibrium landscapes. Interestingly, this possibility exists if envisioning the energetic exponential term of Arrhenius rate constants as the probability that the energy of the reactant is sufficient for the transition. This radically new approach encompasses Maxwell–Boltzmann distributions and solves inconsistencies in previous theories, in particular on the role of temperature in kinetics and thermodynamics. These probabilistic rate constants are then reintroduced in dynamic systems to provide them with the two distinct facets of time: the time step and the time arrow.

Mode selection of magneto-Rayleigh-Taylor instability from the point of view of Landau phase transition theory

A theoretical model referring to mode selection of Z-pinch-driven magneto-Rayleigh-Taylor (MRT) instability, which explains the generation of fundamental instability mode and evolution of fundamental wavelength in experiments, is proposed on the basis of the Landau theory of phase transition. The basic idea of this phase transition model lies in that the appearance of MRT instability pattern can be considered as a consequence of the spontaneous generation of interfacial structure like the spontaneous magnetization in a ferromagnetic system. It is demonstrated that the amplitude of instability is responsible for the order parameter in the Landau theory of phase transition and the fundamental wavelength appears to play a role analogous to inverse temperature in thermodynamics. Further analysis indicates that the MRT instability is characterized by first order phase transition and the fundamental wavelength is proportional to the square root of energy entering into the system from the driving source. The theory predicts that the fundamental wavelength grows rapidly and saturates reaching a limiting wavelength of the order of the liner's final outer radius. The results given by this theory show qualitative agreement with the available experimental data of MRT instability of liner implosions conducted on the Sandia Z machine as well as Primary Test Stand facility at the Institute of Fluid Physics.

Energy repartition in the nonequilibrium steady state

The concept of temperature in nonequilibrium thermodynamics is an outstanding theoretical issue. We propose an energy repartition principle that leads to a spectral (mode-dependent) temperature in steady-state nonequilibrium systems. The general concepts are illustrated by analytic solutions of the classical Heisenberg spin chain connected to Langevin heat reservoirs with arbitrary temperature profiles. Gradients of external magnetic fields are shown to localize spin waves in a Wannier-Zeemann fashion, while magnon interactions renormalize the spectral temperature. Our generic results are applicable to other thermodynamic systems such as Newtonian liquids, elastic solids, and Josephson junctions.

Gravel threshold of motion: a state function of sediment transport disequilibrium?

Abstract. In most sediment transport models, a threshold variable dictates the shear stress at which non-negligible bedload transport begins. Previous work has demonstrated that nondimensional transport thresholds (τc*) vary with many factors related not only to grain size and shape, but also with characteristics of the local bed surface and sediment transport rate (qs). I propose a new model in which qs-dependent τc*, notated as τc(qs)*, evolves as a power-law function of net erosion or deposition. In the model, net entrainment is assumed to progressively remove more mobile particles while leaving behind more stable grains, gradually increasing τc(qs)* and reducing transport rates. Net deposition tends to fill in topographic lows, progressively leading to less stable distributions of surface grains, decreasing τc(qs)* and increasing transport rates. Model parameters are calibrated based on laboratory flume experiments that explore transport disequilibrium. The τc(qs)* equation is then incorporated into a simple morphodynamic model. The evolution of τc(qs)* is a negative feedback on morphologic change, while also allowing reaches to equilibrate to sediment supply at different slopes. Finally, τc(qs)* is interpreted to be an important but nonunique state variable for morphodynamics, in a manner consistent with state variables such as temperature in thermodynamics.

Dynamical Casimir effect and minimal temperature in quantum thermodynamics

We study the fundamental limitations of cooling to absolute zero for a qubit, interacting with a single mode of the electromagnetic field. Our results show that the dynamical Casimir effect, which is unavoidable in any finite-time thermodynamic cycle, forbids the attainability of the absolute zero of temperature, even in the limit of an infinite number of cycles.

Thermodynamic and kinetic studies on the deposition of silicon carbon nitride from CH3SiCl3–C3H6–NH3–H2–Ar and its excellent electromagnetic absorbing property

Thermodynamics phase diagram of co-deposited C, SiC and Si3N4 from precursors of CH3SiCl3–C3H6–NH3–H2–Ar was investigated by using FactSage software and its embedded database. The yield of condensed phases in the co-deposition process was examined as the functions of the inject reactant ratios of C3H6/MTS, NH3/MTS and H2/MTS, and the temperature at a fixed pressure of 0.01atm. The thermodynamic study was used to conduct and determine the deposition condition of silicon carbon nitride (SiCN) in the experimental process. The results show that C–SiC, C–SiC–Si3N4 and C–Si3N4 can be co-deposited by adjusting the reactant ratios and temperature in thermodynamics. In kinetics, SiCN ternary phase was successfully deposited in the porous Si3N4 preform by chemical vapor infiltration and chemical vapor deposition when T=800°C, P=0.01atm, [NH3]/[MTS]=0.5 and [C3H6]/[MTS]=0.2–0.6. The surface morphology of the as-prepared SiCN presented the dense convex cell structure, and the rod-like Si3N4 in preform was uniformly covered by SiCN. The dielectric and electromagnetic (EM) properties of Si3N4–SiCN ceramics were evaluated in 8.2–12.4GHz (X-band). With the increase of [C3H6]/[MTS] in the precursors, the content of carbon element and the intensity of Si–C bond in SiCN gradually increased, which made the permittivity, dielectric loss and EM shielding effectiveness of ceramics gradually increase and the EM reflection coefficient decrease. It is confirmed that the novel and component-designable SiCN ceramics possess the excellent EM absorbing property, offering a great possibility as the high-temperature matrix and coating candidate of ceramics matrix composites combining the structural and functional properties.

Unbounded Probability Theory and Its Applications

The order statistics and empirical mathematical expectation (also called the estimate of mathematical expectation in the literature) are considered in the case of infinitely increasing random variables. The Kolmogorov concept, which he used in the theory of complexity, and the relationship with thermodynamics, which was pointed out already by Poincaré, are considered. We compare the mathematical expectation (which is a generalization of the notion of arithmetical mean, and is generally equal to infinity for any increasing sequence of random variables) with the notion of temperature in thermodynamics while deploying a certain analogue of nonstandard analysis. It is shown that there is a relationship with the Van der Waals law of corresponding states. A number of applications of this concept in economics, in internet information networks, and self-teaching systems are also considered.

PHYSICAL TEMPERATURE AND PRESSURE IN FULLY NONEXTENSIVE STATISTICAL THERMODYNAMICS

This paper generalizes previous results concerning the definitions of physical temperature and pressure in nonextensive statistical thermodynamics. The novelty is that both the internal energy and the volume are no longer additive functions. The new approach is referred to as "fully" nonextensive thermodynamics. The physical temperature is different from the inverse of the Lagrange multiplier. This fact changes the form of some usual thermodynamic relations. For example, the Clausius definition of the thermodynamic entropy has to be modified. As an application, the classical gas model is examined with statistical calculations performed under the Tsallis–Mendes–Plastino formalism of nonextensive thermodynamics. The specific heat expression differs from the one encountered in ordinary extensive thermodynamics but the equation of state keeps the same form.

Application of analytical thermodynamics: relativistic transformation of temperature in equilibrium thermodynamics

Relativistic transformation of temperature in equilibrium thermodynamics can again be studied with a new view point and method of analytical thermodynamics, and the same result of T=1-β2T0 obtained by Planck, Eins tein or de Broglie can again be obtained. In analytical thermodynamics, its characteristic or adva ntage is that the disputed relativistic transformation δQ=1-β2 δQ0 and the obvious relativistic transformation p=p0 are not needed, they are by-products in the derivation.

Two-pion interferometry at small relative momentum for pion sources with transverse and longitudinal expansions in relativistic heavy ion collisions

A two-pion correlation function at small relative momentum for pion sources with transverse and longitudinal expansions in relativistic heavy ion collisions is obtained using two-pion interferometry at small relative momentum and the relations between the real and apparent parameters of the pion source are given. The relations can be used to extract both the temperature and the transverse and longitudinal expansion velocities of pion sources and to verify the correctness of relativistic transformation T' = T(1−v2)1/2 of temperature in relativistic statistical mechanics and thermodynamics.

Entropy of fluidized bed—a measure of particles mixing

The paper presents an attempt to define the physical entropy of the dense phase of a fluidized bed, based on liquid-like properties of fluidized systems. The quantity U was used as the analogy of temperature in classical thermodynamics. The obtained expression for physical entropy was compared to the correlation suggested for the Kolmogorov entropy in bubbling bed.

Measuring nonequilibrium temperature of forced oscillators.

The meaning of temperature in nonequilibrium thermodynamics is considered by using a forced harmonic oscillator in a heat bath, where we have two effective temperatures for the position and the momentum, respectively. We propose a concrete model of a thermometer to testify the validity of these different temperatures from the operational point of view. It is found that the measured temperature depends on a specific form of interaction between the system and a thermometer, which means that the zeroth law of thermodynamics cannot be immediately extended to nonequilibrium cases.

An unattainability conjecture

It is suggested that limits to the variation of physical variables are themselves unattainable, though they can be approached as closely as desired. This general unattainability principle is illustrated in various ways. It leads on to a study of how toremoveinfinities in physics when they cause conceptual problems, and how tointroduceinfinities or zeros for those boundary points in physics which are in some sense unattainable. An analogy between temperature in thermodynamics and time in cosmology is pointed out for the case when boundary points are involved.

Relativistic σ-ω model at finite temperature in thermo field dynamics

Properties of hot and/or dense hadronic matter are studied with the relativistic σ-ω model in the framework of thermo field dynamics - a real-time formalism of finite-temperature field theory free from ( δ( p 2 − m 2)) n -type singularity in perturbation expansion. A unified description of zero- and nonzero-temperature matter is presented. The equation of state is obtained in the Hartree-Fock (HF) as well as in the Hartree approximation at temperatures up to 200 MeV for nuclear matter and up to 20 MeV for neutron matter; the HF calculation shows that the “dressed” nucleon is stable at these temperatures even if the contribution of exchange terms is taken into account. The heat capacity of nuclear matter at low temperature is also calculated.