Aspects of statistical thermodynamics

The equipartition theorem, which describes the correlation structure of the variables of a Hamiltonian system in the NVT ensemble, is a central component of the held of statistical mechanics. Although the intent of this chapter is to introduce aspects of statistical thermodynamics essential for the remainder of this book -and not to be a complete text on statistical mechanics - the equipartition theorem provides an interpretation of the intrinsic variable T that is useful in guiding our intuition about temperature in chemical reaction systems. 

Molecular modeling has reached into many domains of science and technology. One area that has a rich history of applied theory is polymer science. Indeed, many aspects of statistical thermodynamics were developed in an attempt to understand polymer systems. Unfortunately, many theories provide only macroscopic views of polymer systems and are sometimes out of date. 

We have explored some of the simpler aspects of statistical thermodynamics, a very powerful theoretical tool. If the energy levels of the molecules composing the system can be obtained by solution of the Schrodinger equation, the partition function can be calculated then any thermodynamic property can be evaluated. One of the great virtues of statistical thermodynamics is its ability to reveal general laws. For example, we reached the conclusion that all monatomic solids should have the same heat capacity at high temperatures. Restrictions on the laws are made apparent f or example, the heat capacity of a monatomic solid at low temperatures depends on what is assumed about the frequencies in the solid. 

The main theoretical framework of the static aspect of statistical thermodynamics is Gibbs statistical mechanics. The universal behavior of macroscopic objects... 

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