Table 1 Summary of the DynMaxEnt approach in four steps
Step 1Formulate dynamics, as in (1), for the probability distribution of the state variables Embedded Image.
Step 2Obtain the stationary distribution ψ and write it in an exponential (log-linear) form Embedded Image in terms of observables Embedded Image and constant forces α.
Step 3Represent Embedded Image as a solution of a variational MaxEnt problem with reference distribution Embedded Image, constraints on Embedded Image, and Lagrange multipliers α (nonunique).
Step 4Use 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 Embedded Image.