Elements of statistical mechanics

Thermodynamics, as we have studied it so far, is referred to as Qassical Thermodynamics and is built upon its empirical laws. They are called empirical because they are the results of observations through the years (Chapter 4) and their validity lies with the fact that they have never failed. 

Using these laws and the three concepts (properties) introduced by them temperature, internal energy, and entropy, along with the auxiliary ones enthalpy, free energies, heat capacity, etc., the whole building of thermodynamics is constructed. 

classical thermodynamics provides no clues about the origin of these laws, especially of the more complex second one, or any methods for determining these properties. 

Is there a rigorous, from first principles, development of the second law (and perhaps something deeper, or more profound philosophically, in it) and 

1s there an avenue for the evaluation of various thermodynamic properties without having to resort to experimental measurements, as is the case with the classical approach  

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D. ter Haar, Elements of Statistical Mechanics, Holt, Rinehart, and Winston, New York, 1954 W. Band, Introduction to Quantum Statistics, D. Van Nostrand Co., Inc., Princeton, N.J., 1955. 

The previous section reviewed the elements of statistical mechanics that are important in thinking about the structures, fluctuations, and phase behavior of surfaces, interfaces, and membranes. In this section, we consider an important application of these ideas to the problem of phase separation in binary mixtures. This problem is analogous to other types of phase transitions, such as those found in Ising magnets. It is important to understand the specific problem of phase separation because it is this phenomenon that results in the equilibrium between two coexisting states, which naturally gives rise to the existence of interfaces. 

This chapter surveys some of the basic elements of statistical mechanics necessary for the development of the subject matter in the subsequent chapters. Most of the material in this chapter is presumed to be known to the reader. The main reason for presenting it here is to establish a unified system of notation which will be employed throughout the book. 

D. Ter Haar Elements of Statistical Mechanics (Pergamon, New York 1977)... 

D. ter Haar, Elements of Statistical Mechanics (New York Rinehart, 1954), pp. 381-382. A. Messiah, Quantum Mechanics, translation by J. Potter (Amsterdam North-Holland, nn e Mr-(nS. 

Tee Haar, B., Elements of Statistical Mechanics, Rinehart, New York (1954). 

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