Fluctuation of mean Lyapunov exponent for a coupled map lattice model

Fluctuation of mean Lyapunov exponent for the coupled map lattice of logistic map is studied. Theorem by Gallavotti and Cohen for many particle systems is applied to the coupled map lattice model. It is shown that the fluctuation of mean Lyapunov exponent for the model satisfies the extended form of the fluctuation theorem by them. The concept of the mean Lyapunov exponent introduced in this paper turns out to be realistic as well as the one for many particle systems. As a result, the relation between mean Lyapunov exponent and entropy production rate is derived.