Thermodynamics microscopic foundation

MSN.77. 1. Prigogine, Microscopic aspects of entropy and the statistical foundations of nonequilibrium thermodynamics. Proceedings, International Symposium on Foundations of Continuum Thermodynamics, Bussaco, Delgado Domingo, M. N. R. Nina and J. H. Whitelaw, eds., Lisboa, 1974,... 

Linear response theory is an example of a microscopic approach to the foundations of non-equilibrium thermodynamics. It requires knowledge of the Hamiltonian for the underlying microscopic description. In principle, it produces explicit formulae for the relaxation parameters that make up the Onsager coefficients. In reality, these expressions are extremely difficult to evaluate and approximation methods are necessary. Nevertheless, they provide a deeper insight into the physics. 

The foundations of thermodynamics rest on two laws. The first law of thermodynamics defines a function of state, the energy, and restricts the region of conceivable processes to those in which the energy is conserved. The second law determines the direction in which the possible processes will proceed in a given system. These laws represent the formalization of a large number of experimental observations. No violations of these laws have been observed, and it is clear, from microscopic statistical mechanical considerations, that the occurrence of such violations is so improbable that they may be considered to be impossible. 

Statistical mechanics forms the foundation of the methodological developments of the free energy difference techniques, providing the link between macroscopic, measurable quantities of chemical systems, and the detailed, microscopic description of the molecular system. The thermodynamic quantities of interest are expressed in terms of ensemble averages, phase space probabilities or partition functions, all of which eventually are determined by the system Hamiltonian. The main difficulty in practical calculations does not lie in... 

The basic, macroscopic theories of matter are equilibrium thermodynamics, irreversible thermodynamics, and kinetics. Of these, kinetics provides an easy link to the microscopic description via its molecular models. The thermodynamic theories are also connected to a microscopic interpretation through statistical thermodynamics or direct molecular dynamics simulation. Statistical thermodynamics is also outlined in this section when discussing heat capacities, and molecular dynamics simulations are introduced in Sect 1.3.8 and applied to thermal analysis in Sect. 2.1.6. The basics, discussed in this chapter are designed to form the foundation for the later chapters. After the introductory Sect. 2.1, equilibrium thermodynamics is discussed in Sect. 2.2, followed in Sect. 2.3 by a detailed treatment of the most fundamental thermodynamic function, the heat capacity. Section 2.4 contains an introduction into irreversible thermodynamics, and Sect. 2.5 closes this chapter with an initial description of the different phases. The kinetics is closely link to the synthesis of macromolecules, crystal nucleation and growth, as well as melting. These topics are described in the separate Chap. 3. 

We have reviewed here the simplest, isothermal version of CDLG models for two-phase fluid dynamics on the microscopic scale. Applications of these models for studying interfacial dynamics in liquid-vapor and liquid-liquid systems in microcapillaries were discussed. The main advantage of our approach is that it models the exphcit dependence of the interfadal structure and dynamics on molecular interactions, including surfactant effects. However, an off-lattice model of microscopic MF dynamics may be required for incorporating viscoelastic and chain-connectivity effects in complex fluids. Isothermal CDLG MF dynamics is based on the same local conservation laws for species and momenta that serve as a foundation for mechanics, hydrodynamics and irreversible thermodynamics. As in hydrodynamics and irreversible thermodynamics, the isothermal version of CDLG model ean be... 

This equation is the historical foundation of statistical mechanics. It connects the microscopic and macroscopic worlds. It defines the entropy S, a macroscopic quantity, in terms of the multiplicity W of the microscopic degrees of freedom of a system. For thermodynamics, k = 1.380662 x is a... 

Looking at the phase space not as a succession in time of microscopic states that follow Newtonian mechanics, but as an ensemble of microscopic states with probabilities that depend on the macroscopic state, Gibbs and Boltzmann set the foundation of statistical thermodynanucs, which provides a direct connection between classical thermodynamics and microscopic properties. 

Indeed in classical mechanics with a continuum phase space, there exists an inhnitely large collection of microscopic systems that correspond to a particular macroscopic state. Gibbs named this collection of points in phase space an ensemble of systems. Gibbs then shifted the attention from trajectories, i.e., a succession of microscopic states in time, to all possible available state points in phase space that conform to given macroscopic, thermodynamic constraints. He then defined the probability of each member of an ensemble and determined thermodynamic properties as averages over the entire ensemble. In this chapter, we present the important elements of Gibbs ensemble theory, setting the foundation for the rest of the book. 

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