Reversible Transformations and Information

But there lie twin cruxes. A reversible path marks a locus of nearest-neighbor state points there is virtually an infinite number in the general case. Information in Chapter 2 was grounded on finite state collections—coin faces, peptides, and so forth. By contrast, formulae such as Equations (4.25A) and (4.25B) specify infinitudes of pF states, and accordingly, fact and data information. 

The second crux concerns probability. This was defined in Chapter 2 in terms of infinite trials and measurements. Once in place, the probability distributions never wavered for a system of interest. 

Thermodynamic systems and pathways pose a very different situation. Assessing a point locus for information in the statistical sense requires the chemist to view the system in finite-resolution, objective terms. Information is quantified as a result of logical predictions of answers to yes or no questions. The basis for a prediction is 

Chemical Thermodynamics and Information Theory with Applications 

Yet by the condition of reversibility, the system must maintain equilibrium within itself and with the surroundings at all stages. Equilibrium states are like coins that lie flat on a table or like an isolated peptide to one critical extent they offer zero testimony about the history or future. Therefore, while the chemist has a firm grasp of the collection of states, he or she is not spared the uncertainty that would precede any and all measurements. The chemist is pathwaywise he or she is 100% sure that that measured p or V will lie somewhere within certain boundaries. But the chemist is ignorant of the state arrival, dwell, and departure times. There is doubt consequently attached to inquiries about the state at any instant. 

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