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Information dynamics in quantum theory. (English) Zbl 1139.81017
Summary: Shannon entropy and Fisher information functionals are known to quantify certain information-theoretic properties of continuous probability distributions of various origins. We carry out a systematic study of these functionals, while assuming that the pertinent probability density has a quantum mechanical appearance \(\rho \dot = |\psi|^2\), with \(\psi\in L^2(\mathbb R)\). Their behavior in time, due to the quantum Schrödinger picture evolution induced dynamics of \(\rho(x, t)\) is investigated as well, with an emphasis on thermodynamical features of quantum motion.
81P68 Quantum computation
94A17 Measures of information, entropy
81P05 General and philosophical questions in quantum theory
80A05 Foundations of thermodynamics and heat transfer