Equilibrium States, Pathways, and Measurements

There were three themes of the previous chapter. First was the infrastructure for describing systems via potentials, state variables, and differentials. Second was the use of empirical equations to model systems at equilibrium. Third, was that fluctuations impose a nonzero width on every state point. A point anticipated by the ideal gas, van der Waals, or other equations of state is not infinitely sharp as in analytic geometry. Rather, a system demonstrates a range of pressure, density, and other properties. The fluctuations are as integral to the thermodynamic behavior as the average values. 

Chemical Thermodynamics and Information Theory with Applications 

FIGURE 4.1 Reprise of Chapter 3 themes. The upper portion depicts a gas at equilibrium. Because of energy exchanges and other fluctuations, the state point for the system demonstrates a finite width as in the lower panel. 

FIGURE 4.2 Pathway structure of a state point. A system does not demonstrate island points as in region A. Rather, the states are linked one to another by equilibrium fluctuations. A succession of points as in region B traces a pattern evocative of Brownian motion. The pathway structure is ordinarily undetectable given the typical measurement resolution window Ap and AV. 

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