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On Fisher Information and Thermodynamics
Citation:
CABEZAS, H. On Fisher Information and Thermodynamics. Presented at 2008 Annual Meeting of the American Institute of Chemical Engineers, Philadelphia, PA, November 16 - 21, 2008.
Impact/Purpose:
To inform the public
Description:
Fisher information is a measure of the information obtainable by an observer from the observation of reality. However, information is obtainable only when there are patterns or features to observe, and these only exist when there is order. For example, a system in perfect disorder has no patterns or features from which information can be obtained, and the Fisher information obtained from observation of the system would approach zero. Contrarily, a system in perfect order would have very well defined patterns and features, and the Fisher information obtainable from observing the system would approach a maximum. To the extent that entropy is a measure of disorder, as the entropy of the universe increases with time according to the Second Law of Thermodynamics, the Fisher information decreases, but not in a simple reciprocal manner. Further, as the entropy approaches zero for a perfect crystal at 0 K, the Fisher information approaches a maximum. Fisher information, therefore, follows its own version of the Second and Third Laws of Thermodynamics. These arguments will be explored for systems of many molecules starting from the work of Boltzmann, Planck, and others, and an expression for computing the Fisher information from the canonical partition function will be presented. Fisher information is, however, qualitatively different from entropy and potentially possessing a great deal more structure. This will be illustrated with results from classic thought experiments such as the mixing of pure fluids. Here, while the entropy of isochorically mixing two pure ideal gases is always positive and depends only on the respective number of moles of the two gases, the Fisher information of mixing has far more structure involving the mole numbers and molecular masses. The general objective is to explore Fisher information as a thermodynamic property, and to stimulate further investigation into a new line of thought in the area of Thermodynamics.
