  The dynamical entropy on von Neumann algebras defined by Accardi, Ohya and
Watanabe (AOW entropy) is a natural noncommutative extension of the classical
dynamical entropy. On the other hand, quantum spin lattice systems currently
used in quantum computing and communication processes are mathematically
described by $C^*$-algebras called CAR algebras. Therefore, in order to obtain
the average amount of quantum information and to calculate the uncertainty of
the dynamics of quantum spin systems, it is necessary to define dynamical
entropy on CAR algebras. In this paper, we formulate dynamical entropy on CAR
algebras based on the construction of the AOW entropy. Moreover, we compute the
introduced entropy for a $2 \times 2$ matrix algebra case which has relation to
the quantum spin system.
