Statistical thermodynamics large deviations

Statistical Thermodynamics of Chalcogenides with Large Stoichiometric Deviations... 

To imderstand systems consisting of many elements with the aid of thermodynamics and mechanics is the objective of statistical thermod5mamics. The advent of single macromolecule experimental methods emphasizes the importance of the study of mesoscopic systems and fluctuations. Macroscopic and mesoscopic observables (henceforth simply called macro-observables) are interpreted as sums of many microscopic quantities or coarse-grained stochastic quantities. Thus, elucidating macroscopic or mesoscopic behavior in terms of the properties of elements inevitably becomes statistical. The laws of large numbers and the large deviation principle (8) become the key mathematical tools. 

If we look at a small portion of a macroscopic system or study a mesoscopic system, we must study fluctuations. The probability of fluctuations is phenomenologically described by the thermodynamic theory of fluctuations (5). From the ensemble theory point of view, the fluctuation theory is the study of large deviations from the expectation value. This is the reason why large deviation theory is becoming increasingly important in statistical thermodynamics. Standard works on large deviation theory are References 16 and 17 perhaps as accessible introduction to the topic may be found in Reference 18. 

The third law of thermodynamics, like the first and second laws, is a postulate based on a large number of experiments. In this chapter we present the formulation of the third law and discuss the causes of a number of apparent deviations from this law. The foundations of the third law are firmly rooted in molecular theory, and the apparent deviations from this law can be easily explained using statistical mechanical considerations. The third law of thermodynamics is used primarily for the determination of entropy constants which, combined with thermochemical data, permit the calculation of equilibrium constants. 

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