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

Note on entropy dynamics in the Brownian SYK model