Entropy, Chaos, and Quantum Mechanics

Abstract

A characteristic feature of quantum theory is the nontrivial manner in which information about a quantum system is inferred from measurements. These measurements are in general incomplete and do not provide an exhaustive determination of the state of the system. Incomplete information is thus an inherent feature of microphysics and naturally calls for the application of entropie methods. Such methods have in recent years been successfully applied to a number of important problems in quantum dynamics. Here, we will concentrate on a recent formulation of chaos using entropic methods. This formalism, which is equally valid for classical and quantum dynamics, provides a new way of extracting Lyapunov exponents from measured or computed data. The basic quantity is the measurement entropy associated with a dynamical variable of the system, the characteristic exponents being related to the asymptotic growth rate of this entropy. Examples of the use of this method in quantum and classical dynamics, as well as a recent demonstration of the absence of sensitivity to initial conditions in quantum mechanics are discussed. Other applications of entropie methods such as the quantum maximum entropy principle, quantum thermodynamics, and decay of correlations in an open system are briefly recalled.