  We study the time evolution of R\'enyi entropy in a system of two coupled
Brownian SYK clusters evolving from an initial product state. The R\'enyi
entropy of one cluster grows linearly and then saturates to the coarse grained
entropy. This Page curve is obtained by two different methods, a path integral
saddle point analysis and an operator dynamics analysis. Using the Brownian
character of the dynamics, we derive a master equation which controls the
operator dynamics and gives the Page curve for purity. Insight into the physics
of this complicated master equation is provided by a complementary path
integral method: replica diagonal and non-diagonal saddles are responsible for
the linear growth and saturation of R\'enyi entropy, respectively.
