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Fisher Information, Entropy, and the Second and Third Laws of Thermodynamics
CABEZAS, H. AND A. T. Karunanithi. Fisher Information, Entropy, and the Second and Third Laws of Thermodynamics. Donald R. Paul (ed.), INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH. American Chemical Society, Washington, DC, 47(15):5243-5249, (2008).
We propose Fisher Information as a new calculable thermodynamic property that can be shown to follow the Second and the Third Laws of Thermodynamics. Fisher Information is, however, qualitatively different from entropy and potentially possessing a great deal more structure. Hence, a Mathematical expression for computing the Fisher Information of a system of many molecules from the canonical partition function is derived. This development is further illustrated through the derivation of Fisher Information expressions for a pure ideal gas and an ideal gas mixture. Some of the unique properties of Fisher Information are then explored through the classic experiment of the isochoric mixing of two ideal gases. It is worth noting that while the entropy of isochorically mixing two 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. While the application of Fisher Information to molecular systems is clearly in its infancy, it is hoped that the present work will catalyze further investigations into a truly unique line of thought on Thermodynamics.
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Organization:U.S. ENVIRONMENTAL PROTECTION AGENCY
OFFICE OF RESEARCH AND DEVELOPMENT
NATIONAL RISK MANAGEMENT RESEARCH LABORATORY
SUSTAINABLE TECHNOLOGY DIVISION
SUSTAINABLE ENVIRONMENTS BRANCH