MaxEnt and dynamical information

The MaxEnt solutions are shown to display a variety of behaviors (beyond the traditional and customary exponential one) if adequate dynamical information is inserted into the concomitant entropic-variational principle. In particular, we show both theoretically and numerically that power laws and power laws with exponential cut-offs emerge as equilibrium densities in proportional and other dynamics.

💡 Research Summary

The paper revisits the Maximum Entropy (MaxEnt) principle, traditionally used to infer probability distributions under static constraints such as prescribed means or variances, and demonstrates that the inclusion of dynamical information as additional constraints dramatically broadens the class of equilibrium distributions that can be derived. The authors argue that many real‑world complex systems evolve according to specific dynamical rules—proportional growth, linear damping, nonlinear drift, etc.—and that these rules can be encoded directly into the variational formulation of MaxEnt.

Starting from the Shannon entropy functional (S