MaxEnt and dynamical information

TL;DR

This paper demonstrates that incorporating dynamical information into the MaxEnt framework leads to a variety of equilibrium distributions, including power laws and exponential cut-offs, beyond the traditional exponential form.

Contribution

It reveals how dynamical information modifies MaxEnt solutions, producing diverse equilibrium distributions such as power laws.

Findings

Power laws emerge as equilibrium densities in certain dynamics.

Exponential cut-offs can also appear in the equilibrium distributions.

Theoretical and numerical evidence supports these results.

Abstract

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.