Standard concepts of information theory, including Shannon's entropy, Fisher's information, Jaynes' principle of entropy maximization, Fisher's locality information matrix, and Kullback and Leibler's information measure, are described and extended to many dimensions as appropriate, to establish precise connections between the many body quantum‐mechanical kinetic energy functional T[Ψ] and information measures. Implications for density functional theory of electronic structure are discussed, and elementary examples are displayed to illustrate the argument. Among the several exact relations obtained, one of special interest is the identity
where the first term is the intrinsic accuracy or Fisher's information for locality of the one‐particle density (normalized to 1), \documentclass{article}\pagestyle{empty}\begin{document}$ \rho \left( 1 \right) = \int { \cdot \cdot \cdot \int {|{\rm \psi |}^{\rm 2} d_{{\rm T}_2 } \cdot \cdot \cdot } } \,d_{{\rm T}_{\rm N} ,} $\end{document}, and the second term is the average over the one‐particle density of Fisher's information associated with the conditional density \documentclass{article}\pagestyle{empty}\begin{document}$ f\left( {2,\;3,\; \cdot \cdot \cdot ,\;N|1} \right) \equiv \,|\psi |^2 /\rho \left( 1 \right) $\end{document} that is, the second term is the average over the marginal distribution ρ(1) of the trace of Fisher's information matrix for the distribution f(2,3, …, N|1). Because of this formula, the quantum mechanical variation principle may be precisely stated as a principle of minimal information.
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Glycerol and propylene glycol mixtures are common carrier solutions in electronic cigarettes. Aerosols produced from these mixtures will evaporate quickly in a dry environment due to their high volatility. In a humid environment, such as the lungs, the kinetics of evaporation and hygroscopic growth determine the evolution of aerosol plume glycerol. Here, we apply a temperature and relative humidity-controlled hygroscopicity/volatility tandem differential mobility analyzer system to study the growth and evaporation kinetics of glycerol aerosol over a wide range of temperature, relative humidity, and residence times. Results show that at dry conditions glycerol aerosols evaporate within seconds at temperatures warmer than 20 C and that the accommodation coefficient of glycerol vapor on dry glycerol particles is 0.8. Under humidified conditions, the mutual depression of vapor pressures of the aqueous glycerol/water solution slows the glycerol evaporation rate consistent with thermodynamic and kinetic model predictions. Model calculations show that water vapor aided condensation of glycerol can occur at high relative humidity for glycerol vapor concentrations that result in glycerol particle evaporation under dry conditions. The combined results will help with constraining computational modules that model the evolution of glycerol-containing aerosols along a prescribed thermodynamic trajectory.
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