Statistical mechanics’ development

Gibbs, J.W. (1902) Elementary Principles in Statistical Mechanics, Developed with Special Reference to the Rational Foundations of Thermodynamics (Yale University Press, New Haven). 

The chapter starts with a brief review of thermodynamic principles as they apply to the concept of the chemical equilibrium. That section is followed by a short review of the use of statistical thermodynamics for the numerical calculation of thermodynamic equilibrium constants in terms of the chemical potential (often designated as (i). Lastly, this statistical mechanical development is applied to the calculation of isotope effects on equilibrium constants, and then extended to treat kinetic isotope effects using the transition state model. These applications will concentrate on equilibrium constants in the ideal gas phase with the molecules considered in the rigid rotor, harmonic oscillator approximation. 

It is noteworthy that Gibbs himself was acutely aware of the qualitative failures of 19th-century molecular theory (as revealed, for example, by erroneous classical predictions of heat capacities Sidebar 3.8). In the preface to his Elementary Principles in Statistical Mechanics, Developed with Especial Reference to the Rational Foundation of Thermodynamics (published in the last year of his life), Gibbs wrote ... 

Gibbs, J.W. Elementary principles in statistical mechanics, developed with essential reference to the rational foundation of thermodynamics. N.Y. (1902). 

Gibbs JW (1902) Elementary Principles in Statistical Mechanics Developed with especial reference to the rational fundation of thermodynamics. Charles Scribner s Sons, New York... 

The notion of an on,scmble was first suggested by Gibbs in a remarkably insightful manner. In the preface of his book Elementary Principles in Statistical Mechanics Developed with Special Reference to the Rational Foundation of Thermodynamics Gibbs writes [29] ... 

Our intention is to invoke the tools of statistical mechanics developed earlier to quantify these ideas. From the standpoint of our one-dimensional example, the transition rate of eqn (7.54) may be rewritten mathematically as... 

Thus, statistical mechanics development of the thermodynamic laws is interesting and straightforward enough, and it sheds helpful light on thermodynamics. So is the use of information theory to develop and discuss statistical mechanics. They supplement the understanding generated by the macroscopic statements, but in no sense do they replace that understanding. 

Some of the statistical mechanical developments which depend on the power of the computer to carry out the complex calculations are outlined in Sections 10.17 to 10.22 below. Studies on solvation of ions using, in particular, Monte Carlo calculations are given in Chapter 13 on solvation. 

While a quantitative molecular explanation of overcoating in latex polymerization is lacking, a qualitative picture can be synthesized with the aid of the polymer solution statistical mechanics developed by Flory (1953) and the phase separation statistics of Meier (1969, 1970). Let us examine... 

The starting point of the statistical mechanical development in [102] is the notion of a GLG. We define V (r,t) in (30) as the number of particles with velocity C at site r at time t. In contrast with the standard LB model, v, is a (positive) integer in contrast with lattice-gas models, v, > 1. The state at a particular lattice site, v(r,t), is modified by the collision process, subject to the constraints of mass and momentum conservation the post-collision state, v (r,t), is then propagated to the neighboring sites (30). 

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