The geometric entropy is a localized contribution to the entropy obtained using Euclidean gravity methods. In this talk, I will discuss the Hamiltonian flow generated by the geometric entropy operator in general theories of gravity using Lorentzian methods of the Peierls/Poisson brackets. I will discuss examples with higher derivative corrections to illustrate the general features of the geometric flow. In the context of AdS/CFT, I will discuss the connection to modular flow.