Quantization: Non-commutative dynamical entropy

Nowadays quantization is a popular field and several efforts have already been done to quantize the notion of dynamical entropy [6, 9, 10]. In this paper, we explain another way to define dynamical entropy for quantum systems by mapping the dynamical system on a quantum spin chain. We show that in the case of classical systems, one recovers the Kolmogorov-Sinai invariant.