Statistical-mechanics-based

Cao, J., Voth, G.A. The formulation of quantum statistical mechanics based on the Feynman path centroid density. I. Equilibrium properties. J. Chem. Phys. 100 (1994) 5093-5105 II Dynamical properties. J. Chem. Phys. 100 (1994) 5106-5117 III. Phase space formalism and nalysis of centroid molecular dynamics. J. Chem. Phys. 101 (1994) 6157-6167 IV. Algorithms for centroid molecular dynamics. J. Chem. Phys. 101 (1994) 6168-6183 V. Quantum instantaneous normal mode theory of liquids. J. Chem. Phys. 101 (1994) 6184 6192. 

Spin orbitals, 258, 277, 279 Square well potential, in calculation of thermodynamic quantities of clathrates, 33 Stability of clathrates, 18 Stark effect, 378 Stark patterns, 377 Statistical mechanics base, clathrates, 5 Statistical model of solutions, 134 Statistical theory for clathrates, 10 Steam + quartz system, 99 Stereoregular polymers, 165 Stereospecificity, 166, 169 Steric hindrance, 376, 391 Steric repulsion, 75, 389, 390 Styrene methyl methacrylate polymer, 150... 

This begs the question of whether a comparable law exists for nonequilibrium systems. This chapter presents a theory for nonequilibrium thermodynamics and statistical mechanics based on such a law written in a form analogous to the equilibrium version ... 

Cao, J. Voth, G.A., The formulation of quantum statistical mechanics based on Feynman path centroid density, J. Chem. Phys. 1994,100, 5093-5105... 

A Statistical Mechanics Based Lattice Model Equation of State... 

A Statistical-Mechanics based Lattice-Model Equation of state (EOS) for modelling the phase behaviour of polymer-supercritical fluid mixtures is presented. The EOS can reproduce qualitatively all experimental trends observed, using a single, adjustable mixture parameter and in this aspect is better than classical cubic EOS. Simple mixtures of small molecules can also be quantitatively modelled, in most cases, with the use of a single, temperature independent adjustable parameter. 

A statistical-mechanics based model for mixtures of molecules of disparate sizes has been presented in this paper. Results obtained to date demonstrate that the lattice EOS is probably more suited for modelling polymer-SCF equilibria than a modified cubic EOS, while for the other systems, outside the critical region, it performs as well as classically employed techniques. 

Foundation of Equilibrium Statistical Mechanics Based on Generalized Entropy... 

The general mathematical formulation of the equilibrium statistical mechanics based on the generalized statistical entropy for the first and second thermodynamic potentials was given. The Tsallis and Boltzmann-Gibbs statistical entropies in the canonical and microcanonical ensembles were investigated as an example. It was shown that the statistical mechanics based on the Tsallis statistical entropy satisfies the requirements of equilibrium thermodynamics in the thermodynamic limit if the entropic index z=l/(q-l) is an extensive variable of state of the system. 

In modem physics, there exist alternative theories for the equilibrium statistical mechanics [1, 2] based on the generalized statistical entropy [3-12]. They are compatible with the second part of the second law of thermodynamics, i.e., the maximum entropy principle [13-14], which leads to uncertainty in the definition of the statistical entropy and consequently the equilibrium probability density functions. This means that the equilibrium statistical mechanics is in a crisis. Thus, the requirements of the equilibrium thermodynamics shall have an exclusive role in selection of the right theory for the equilibrium statistical mechanics. The main difficulty in foundation of the statistical mechanics based on the generalized statistical entropy, i.e., the deformed Boltzmann-Gibbs entropy, is the problem of its connection with the equilibrium thermodynamics. The proof of the zero law of thermodynamics and the principle of additivity... 

The aims of this study are to establish the connection between the Tsallis statistics, i.e., the statistical mechanics based on the Tsallis statistical entropy, and the equilibrium thermodynamics and to prove the zero law of thermodynamics. 

The structure of the chapter is as follows. In Section 2, we review the basic postulates of the equilibrium thermodynamics. The equilibrium statistical mechanics based on generalized entropy is formulated in a general form in Section 3. In Section 4, we describe the Tsallis statistics and analyze its possible connection with the equilibrium thermodynamics. The main conclusions are summarized in the final section. 

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... 

Parvan A S. Extensive statistical mechanics based on nonadditive entropy Canonical ensemble. Phys. Lett. A. 2006 360(l) 26-34. 

Ideal-gas heat capacities may be estimated from gas-phase heat-capacity measurements, but more often they are calculated from statistical mechanics based on molecular information, usually obtained by spectroscopy [27-29]. The results of such calculations have been tabulated for many molecules [5,11-15,28-30]. Predictive methods also exist based on molecular structure the leading methods are reviewed in The Properties of Gases Liquids [15], Calculations from one of these methods (that of Benson) are available in the NIST Chemistry Webbook [5],... 

Topics covered include the nature and properties of the surface of a polymer melt, the structure of interfaces between different polymers and between pol5miers and non-polymers, adsorption from polymer solutions, the molecular basis of adhesion and the properties of polymers at liquid surfaces. Emphasis is placed on the common physical principles underlying this wide range of situations. Statistical mechanics based models of the behaviour of polymers near interfaces are introduced, with the emphasis on theory that is tractable and applicable to experimental situations. Experimental techniques for studying polymer surfaces and interfaces are reviewed and compared. 

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