Dynamical TAP equations for non-equilibrium Ising spin glasses

We derive and study dynamical TAP equations for Ising spin glasses obeying both synchronous and asynchronous dynamics using a generating functional approach. The system can have an asymmetric coupling matrix and the external fields can be time-dependent. In the synchronously updated model, the TAP equations take the form of self-consistent equations for magnetizations at time t + 1, given the magnetizations at time t. In the asynchronously updated model, the TAP equations determine the time derivatives of the magnetizations at each time, again via self-consistent equations, given the current values of the magnetizations.