# zbMATH — the first resource for mathematics

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.
##### MSC:
 81P68 Quantum computation 94A17 Measures of information, entropy 81P05 General and philosophical questions in quantum theory 80A05 Foundations of thermodynamics and heat transfer