Step 1 | Formulate dynamics, as in (1), for the probability distribution of the state variables . |

Step 2 | Obtain the stationary distribution ψ and write it in an exponential (log-linear) form in terms of observables and constant forces α. |

Step 3 | Represent as a solution of a variational MaxEnt problem with reference distribution , constraints on , and Lagrange multipliers α (nonunique). |

Step 4 | Use a quasi-stationarity assumption to approximate the dynamics of observables using the stationary distribution where the coefficients α are allowed to change over time to match the correct dynamics of observables. This criterion leads to a reduced dynamical system for the effective coefficients . |

See File S1.