Thermodynamic equilibrium universe

On his initiative, A. G. Doroshkevich and I. D. Novikov [56] constructed a global spectrum of the electromagnetic radiation in the Universe and showed that relic radiation in thermodynamic equilibrium can be found in the centimeter region. The discovery of relic radiation answered the question of what model to choose for the Universe. Ya.B. became an ardent proponent of the theory of a hot Universe (see the 1966 review [26 ]). He was one of the first in the world to understand what a powerful tool relic radiation represented for discovery of the Universe s past. His reviews of 1962-1966, which became the basis for excellent books written later with I. D. Novikov [57-59], contain practically all the ideas which have now become the methods for studying the large-scale structure of the Universe. These include the question of dipole and quadrupole anisotropy, and of angular fluctuations of relic radiation, the problem of nuclear synthesis reactions in the hot Universe, and the quark problem, first raised by Ya.B. together with L. B. Okun and S. B. Pikelner (1965) [11 ]. 

Today the situation has changed. We understand now that the laws of thermodynamics are universal at and near equilibrium, but become highly specific in far-from-equilibrium conditions. We also realize that irreversible processes can become a source of order. We see irreversible processes taking a prominent role in our description and understanding of nature. If the proton, as is thought to be by many physicists, turns out... 

Note that is not the thermodynamic equilibrium constant and k T/h is not a universal frequency for the decomposition of the transition-state complexes into products. 

In Chap. 3 (Sect. 3.6), we discussed limitations of the FREZCHEM model that were broadly grouped under Pitzer-equation parameterization and mathematical modeling. There exists another limitation related to equilibrium principles. The foundations of the FREZCHEM model rest on chemical thermodynamic equilibrium principles (Chap. 2). Thermodynamic equilibrium refers to a state of absolute rest from which a system has no tendency to depart. These stable states are what the FREZCHEM model predicts. But in the real world, unstable (also known as disequilibrium or metastable) states may persist indefinitely. Life depends on disequilibrium processes (Gaidos et al. 1999 Schulze-Makuch and Irwin 2004). As we point out in Chap. 6, if the Universe were ever to reach a state of chemical thermodynamic equilibrium, entropic death would terminate life. These nonequilibrium states are related to reaction kinetics that may be fast or slow or driven by either or both abiotic and biotic factors. Below are four examples of nonequilibrium thermodynamics and how we can cope, in some cases, with these unstable chemistries using existing equilibrium models. 

Conceptually, the dead state can be visualized from several different angles as follows The universe contains a stable system which is composed of many stable materials existing in abundance and whose concentrations can be reasonably assumed to remain invariant (1,2,8,11,12,14,16,17). All the stable materials exist in thermodynamic equilibrium at the temperature, Tq, of 298.15 K, and under the total pressure, PQ, of 1 atm. This state is termed the "dead state" (1,2,8,16,18). The most stable materials, which are in the stable sector of the universe, i.e., the dead state, are termed "datum level materials" and have the availability (exergy) and energy (enthalpy relative to the dead state) of zero the concentration of the datum level material is the datum level concentration. 

If the effective temperature of our defined system is less than the universal radiation background temperature of 2.7 K, transitions between the two levels can be observed in absorption. This is the case with interstellar formaldehyde. Alternatively absorption can be observed against the continuum radiation from a nearby bright source. Spontaneous emission will always occur provided the upper of the two levels is populated, and can be observed if the populations are different. There are, in addition, examples of the exceptional situation in which N2 > N the result of this population inversion is that stimulated emission dominates, and maser emission is observed. Interstellar OH and SiO provide diatomic examples of this unusual situation, as also does interstellar H2O we shall describe the results for OH later in this chapter. Departures from local thermodynamic equilibrium are very common, and the concept of temperature in interstellar gas clouds is not simple this is a major part of astrophysics which is, however, beyond the scope of this book. 

Aqueous electrolytes and the equilibrium constants that define various reactions in low-temperature geochemistry are inexorably linked with the problem of activity coefficients, or the problem of nonideality for aqueous electrolyte solutions. Thermodynamic equilibrium constants, defined by an extrapolation to infinite dilution for the standard state condition (not the only standard state), require the use of activity coefficients. Unfortunately, there is neither a simple nor universal nonideality method that works for all electrolytes under all conditions. This section provides a brief overview of a major subject still undergoing research and development but for... 

In conclusion, let us summarize the main principles of the equilibrium statistical mechanics based on the generalized statistical entropy. The basic idea is that in the thermodynamic equilibrium, there exists a universal function called thermodynamic potential that completely describes the properties and states of the thermodynamic system. The fundamental thermodynamic potential, its arguments (variables of state), and its first partial derivatives with respect to the variables of state determine the complete set of physical quantities characterizing the properties of the thermodynamic system. The physical system can be prepared in many ways given by the different sets of the variables of state and their appropriate thermodynamic potentials. The first thermodynamic potential is obtained from the fundamental thermodynamic potential by the Legendre transform. The second thermodynamic potential is obtained by the substitution of one variable of state with the fundamental thermodynamic potential. Then the complete set of physical quantities and the appropriate thermodynamic potential determine the physical properties of the given system and their dependences. In the equilibrium thermodynamics, the thermodynamic potential of the physical system is given a priori, and it is a multivariate function of several variables of state. However, in the equilibrium... 

In order to derive these we will consider an adiabatic evacuated enclosure, like that shown in Fig. 5.19, with walls of any material. In this enclosure a state of thermodynamic equilibrium will be reached The walls assume the same temperature T overall and the enclosure is filled with radiation, which is known as hollow enclosure radiation. In the sense of quantum mechanics this can also be interpreted as a photon gas in equilibrium. This equilibrium radiation is fully homogeneous, isotropic and non-polarised. It is of equal strength at every point in the hollow enclosure and is independent of direction it is determined purely by the temperature T of the walls. Due to its isotropic nature, the spectral intensity L x of the hollow enclosure radiation does not depend on / and universal function of wavelength and temperature L x = L x X,T), which is also called Kirchhoff s function. As the enclosure is filled with the same diffuse radiation, the incident spectral intensity Kx for every element of any area that is oriented in any position, will, according... 

The fluctuations at thermodynamic equilibrium are related in a universal way to the kinetic response according to the fluctuation-dissipation theorem (FTD). 

Abstract The Gibbs phase rule relating the number of degrees of freedom / of a system to the number of components c and the number of coexisting phases p is a central, universally used relation, expressed by what is probably the simplest formula in the natural sciences,/ = c — p + 2. Research into the behavior of small systems, notably atomic clusters, has shown in recent years that the phase rule is not as all-encompassing as is often assumed. Small systems can show coexistence of two or more phases in thermodynamic equilibrium over bands of temperature and pressure (with no other forces acting on them). The basis of this apparent violation of the phase rule, seeming almost like violation of a scientific law, is in reality entirely understandable, consistent with the laws of thermodynamics, and even allows one to estimate the upper size limit of any particular system for which such apparent violation could be observed. 

This is the Fourier law of heat conduction with the thermal conductivity being k = Cvi 3. Note that we have not made any assumption of the type of energy carrier and, hence, this is a universal law for all energy carriers. The only assumption made is that of local thermodynamic equilibrium such that the energy density u at any location is a function of the local temperature. 

The Larimer-Grossman condensation model has received its share of criticism in the intervening decade. Much of the debate was raised by the assumption that all solid and gaseous species fully equilibrated, which seems unlikely, particularly at lower temperatures. Despite these concerns, the equilibrium picture fits many of the broad scale chemical features of our solar system remarkably well. It certainly demonstrates the power of thermodynamic equilibrium models, considering the size and complexity of the chemical system that is our niche in the universe. 

M. Le Bellac, F. Mortessagne, C. Batrouni, Equilibrium and Non-equilibrium Statistical Thermodynamics, Cambridge University Press, Cambridge, 2004. 

A system in which the dependent variables are constant in time is said to be in a steady or stationary state. In a chemical system, the dependent variables are typically densities or concentrations of the component species. Two fundamentally different types of stationary states occur, depending on whether the system is open or closed. There is only one stationary state in a closed system, the state of thermodynamic equilibrium. Open systems often exhibit only one stationary state as well however, multistability may occur in systems with appropriate elements of feedback if they are sufficiently far from equilibrium. This phenomenon of multistability, that is, the existence of multiple steady states in which more than one such state may be simultaneously stable, is our first example of the universal phenomena that arise in dissipative nonlinear systems. 

The quasi-Fermi level is often interpreted as a thermodynamic driving force. Whether or not this is appropriate is a matter of some debate. While it may provide useful insights, the concept has been derived from kinetic arguments, and can at best provide a quasi-thermodynamic description. Whereas true equilibrium thermodynamics are universally valid, the predictive value of the quasi-Fermi level as a thermodynamic driving force for, e.g., chemical reactions may depend on the reaction mechanism. One particular aspect to be noted in this respect is that the quasi-Fermi level definitions in (2.62) and (2.63) only consider electrons and holes in the conduction and valence bands. They do not account for any changes in the... 

The phase rule is universally valid for systems in thermodynamic equilibrium and establishes the theoretical basis for all phase diagrams. 

Liquid-liquid equilibrium Root mean square deviation Ternary system Thermodynamic models Universal quasi-chemical... 

In the present state of the universe, only a very small part of the energy is in the form of protons, neutrons and electrons that make up ordinary matter in all the galaxies. The rest consists of thermal radiation at a temperature of about 2.8 K and particles called neutrinos that interact very weakly with other particles. The small amount of matter which is in the form of stars and galaxies, however, is not in thermodynamic equilibrium. The affinities for the reactions that are currently occurring in the stars are not zero. The nuclear reactions in the stars produce all the known elements from hydrogen [2-4]. Hence the observed properties such as the abundance of elements in stars and planets cannot be described using the theory of chemical equilibrium. A knowledge of the rates of reaction and the history of the star or planet are necessary to understand the abundance of elements. 

As emphasized earlier, we live in a world that is not in thermodynamic equilihrium. The 2.8 K thermal radiation that fills the universe is not in thermal equilibrium with the matter in the galaxies. On a smaller scale, the earth, its atmosphere, biosphere and the oceans are all in a nonequilibrium state due to the constant influx of energy from the sun. In the laboratory, most of the time we encounter phenomena exhibited by systems not in thermodynamic equilibrium, while equilibrium systems are the exception. 

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