an:05287038
Zbl 1139.81017
Garbaczewski, Piotr
Information dynamics in quantum theory
EN
Appl. Math. Inf. Sci. 1, No. 1, 1-12 (2007).
00208660
2007
j
81P68 94A17 81P05 80A05
information entropy; entropy methods; dynamics of densities; entropy dynamics; Fisher information; indeterminacy relations; entropic inequalities; laws of thermodynamics; Helmholtz free energy; quantum motion
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 Schr??dinger picture evolution induced dynamics of \(\rho(x, t)\) is investigated as well, with an emphasis on thermodynamical features of quantum motion.