  We study and compare the information loss of a large class of Gaussian
bipartite systems. It includes the usual Caldeira-Leggett type model as well as
Anosov models (parametric oscillators, the inverted oscillator environment,
etc), which exhibit instability, one of the most important characteristics of
chaotic systems. We establish a rigorous connection between the quantum
Lyapunov exponents and coherence loss, and show that in the case of unstable
environments coherence loss is completely determined by the upper quantum
Lyapunov exponent, a behavior which is more universal than that of the
Caldeira-Leggett type model.
