The Maximum Entropy Principle in Nonequilibrium Thermodynamics: A Brief History and the Contributions of Wolfgang Dreyer

TL;DR

The paper traces the historical development of the Maximum Entropy Principle (MEP) as a closure method for the moment hierarchy of the Boltzmann equation, foregrounding Wolfgang Dreyer's key classical and relativistic contributions and their alignment with Rational Extended Thermodynamics (RET). It explains how Dreyer extended Kogan's MEP to degenerate gases, and how the MEP closures dovetail with RET near equilibrium for the 13-moment system, unifying kinetic and macroscopic closures. The discussion extends to polyatomic gases, nonlinear MEP closures (e.g., RET6 and eleven-moment ellipsoidal Gaussian), and relativistic generalizations, including how general entropy functionals influence closures and convergence properties. The work also addresses limitations such as the Junk problem and hyperbolicity domains, while highlighting Dreyer's pivotal role in connecting kinetic- and continuum-based nonequilibrium thermodynamics across classical and relativistic regimes.

Abstract

We present a brief history of how the famous Maximum Entropy Principle was used as closure of moments of the Boltzmann equation. In particular, we want to remark on the important role of two fundamental papers by Wolfgang Dreyer, one in the classical framework and one in a relativistic context, to use this principle and to compare the result with the macroscopic theory of Rational Extended Thermodynamics.