Principle of local state

There are three different approaches to a thermodynamic theory of continuum that can be distinguished. These approaches differ from each other by the fundamental postulates on which the theory is based. All of them are characterized by the same fundamental requirement that the results should be obtained without having recourse to statistical or kinetic theories. None of these approaches is concerned with the atomic structure of the material. Therefore, they represent a pure phenomenological approach. The principal postulates of the first approach, usually called the classical thermodynamics of irreversible processes, are documented. The principle of local state is assumed to be valid. The equation of entropy balance is assumed to involve a term expressing the entropy production which can be represented as a sum of products of fluxes and forces. This term is zero for a state of equilibrium and positive for an irreversible process. The fluxes are function of forces, not necessarily linear. However, the reciprocity relations concern only coefficients of the linear terms of the series expansions. Using methods of this approach, a thermodynamic description of elastic, rheologic and plastic materials was obtained. 

The third approach is called the thermodynamic theory of passive systems. It is based on the following postulates (1) The introduction of the notion of entropy is avoided for nonequilibrium states and the principle of local state is not assumed, (2) The inequality is replaced by an inequality expressing the fundamental property of passivity. This inequality follows from the second law of thermodynamics and the condition of thermodynamic stability. Further the inequality is known to have sense only for states of equilibrium, (3) The temperature is assumed to exist for non-equilibrium states, (4) As a consequence of the fundamental inequality the class of processes under consideration is limited to processes in which deviations from the equilibrium conditions are small. This enables full linearization of the constitutive equations. An important feature of this approach is the clear physical interpretation of all the quantities introduced. 

The fundamental hypothesis of CIT is the existence of a local-equilibrium condition. A series of finite volume cells is considered in a material body, in which local variables such as temperature and entropy are uniform and in equilibrium, but time-dependent. The variables can take different values from cell to cell. The majority of textbooks are written using this formulation (see, e.g., Kestin 1979, which refers to this as the principle of local state). The most important result of CIT under the local-equilibrium hypothesis is that, as a natural result of the Second Law of Thermodynamics in the course of a mechano-thermal process, we have the following entropy inequality ... 

Principle of local symmetry. In the interaction between a symmetric or a quasisymmetric monomer and its own active center being in the free-radical or free-ionic state, a cyclic adduct of the donor-acceptor type exhibiting the local pseudosymmetry of the third order is formed as one of the intermediates. 

Central to the EPR paradox is a thought experiment in which two spins are initially coupled to a state with S = 0 and are then separated to a large distance, at which they can be separately observed. Quantum mechanics appMently predicts that the two spins remain forever coupled, but this conflicts with Einstein s principle of locality or separability , according to which spatially well separated systems must be independent, no matter how strongly they have interacted in the past. It is now widely held that Einstein was wrong and that non-locality follows inevitably from quantum mechanics i.e. that even distant systems are never truly separable. 

It is difficult to find indisputable experimental evidence for these processes in noncrystalline semiconductors and insulators. Although in principle the dependence of the current on electrode spacing should distinguish between uniform and nonuniform fields and the dependence on temperature and voltage between the different injection mechanisms, very little has been learnt so far from these experiments about the nature of contacts and the distribution and the density of localized states in NCS. 

Local equilibrium is spoken of when the local values of thermodynamic and optical properties relate to each other as if the substance were in the state of general thermodynamic equilibrium. This principle of local equilibrium underlies hydrodynamics (Landau and Lifshitz, 1988) and unequilibrium thermodynamics (Glansdorff and Prigogine, 1971). 

High-resolution NMR in the solid state of matter has been developed fairly recently. Since this technique can detect the local structure of molecules via chemical shift and magnetic relaxation, it has been possible to obtain detailed information on chain conformation as well as chain dynamics of macromolecules not only in the crystalline state but also in the non-crystalline, glassy or rubbery state. This chapter gives a brief description of the basic principles of solid-state high-resolution NMR as well as its recent application to crystalline polymers. 

Anderson et al. have presented solid-state NMR analysis of local structural environments in phosphate glasses for educational purposes. " In particular, the solid-state NMR wide-line spectra of a series of sodium phosphate glasses have been considered, which can also be simulated by spectral addition of reference solid-state spectra obtained for pure pyrophosphate and metaphosphate salts. The example chosen introduces the principles of solid-state NMR and allows interpretation of the spectrum in terms of the composition and localised phosphate environment. 

A common explanation for such phenomena is that the gradient of the deformation rate tensor affects the flow induced anisotropy and hence the stress. It follows obviously that filled (polymer) systems cannot be "simple" fluids since their behavior, by virtue of their true nature, violates the principle of "local action," which states that the stress in a fluid element is determined by the deformation history of that fluid element and is independent of the history of neighboring elements. This is the main reason for the... 

As a result of simultaneous introduction of elastic, viscous and plastic properties of a material, a description of the actual state functions involves the history of the local configuration expressed as a function of the time and of the path. The restrictions, which impose the second law of thermodynamics and the principle of material objectivity, have been analyzed. Among others, a viscoplastic material of the rate type and a strain-rate sensitive material have been examined. 

Solid mixed ionic-electronic conductors (MIECs) exhibit both ionic and electronic (electron-hole) conductivity. Naturally, in any material there are in principle nonzero electronic and ionic conductivities (a i, a,). It is customary to limit the use of the term MIEC to those materials in which a, and 0, 1 do not differ by more than two orders of magnitude. It is also customary to use the term MIEC if a, and Ogi are not too low (o, a i 10 S/cm). Obviously, there are no strict rules. There are processes where the minority carriers play an important role despite the fact that 0,70 1 exceeds those limits and a, aj,i< 10 S/cm. In MIECs, ion transport normally occurs via interstitial sites or by hopping into a vacant site or a more complex combination based on interstitial and vacant sites, and electronic (electron/hole) conductivity occurs via delocalized states in the conduction/valence band or via localized states by a thermally assisted hopping mechanism. With respect to their properties, MIECs have found wide applications in solid oxide fuel cells, batteries, smart windows, selective membranes, sensors, catalysis, and so on. 

The operation principle of these TFTs is identical to that of the metal-oxide-semiconductor field-effect transistor (MOSFET) [617,618]. When a positive voltage Vg Is applied to the gate, electrons are accumulated in the a-Si H. At small voltages these electrons will be localized in the deep states of the a-Si H. The conduction and valence bands at the SiN.v-a-Si H interface bend down, and the Fermi level shifts upward. Above a certain threshold voltage Vth a constant proportion of the electrons will be mobile, and the conductivity is increased linearly with Vg - Vih. As a result the transistor switches on. and a current flows from source to drain. The source-drain current /so can be expressed as [619]... 

Localized bonding orbitals are then constructed from a linear combination of the orbital on each of the paired atoms. To do this we use the principle of maximum overlap, which states... 

The impurity interacts with the band structure of the host crystal, modifying it, and often introducing new levels. An analysis of the band structure provides information about the electronic states of the system. Charge densities, and spin densities in the case of spin-polarized calculations, provide additional insight into the electronic structure of the defect, bonding mechansims, the degree of localization, etc. Spin densities also provide a direct link with quantities measured in EPR or pSR, which probe the interaction between electronic wavefunctions and nuclear spins. First-principles spin-density-functional calculations have recently been shown to yield reliable values for isotropic and anisotropic hyperfine parameters for hydrogen or muonium in Si (Van de Walle, 1990) results will be discussed in Section IV.2. 

There are other noteworthy single excited-state theories. Gorling developed a stationary principle for excited states in density functional theory [41]. A formalism based on the integral and differential virial theorems of quantum mechanics was proposed by Sahni and coworkers for excited state densities [42], The local scaling approach of Ludena and Kryachko has also been generalized to excited states [43]. 

The conclusion that the local hardness is given entirely by the variable parts of the kinetic energy is very logical. It is the kinetic energy increase which limits the distribution of electron density in all systems with fixed nuclei. Since the equilibrium state of atoms and molecules is characterized by minimum energy, they will also be marked by maximum kinetic energy because of the virial theorem. This will put them in agreement with the principles of maximum hardness, for which much evidence exists. 

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