Information-Theoretic Uncertainty Relation and Random-Phase Entropy

Abstract

Dunkel and Trigger [Phys. Rev. A {71}, 052102 (2005)] show that the Leipnik's joint entropy monotonously increases for the initially maximally classical Gaussian wave packet for a free particle. After expressing the joint entropy of the general Gaussian wave packets for quadratic Hamiltonians as $S(t)=ln(e/2)+ln(2Deltax(t)Deltap(t)/hbar)$, we show that a class of general Gaussian wave packets does not warrant the monotonous increase of the joint entropy. We propose that the random-phase entropy with respect to the squeeze angle always monotonously increases even for non-maximally classical states.

RevTex 4 pages, 4 figures