A unified view of transport equations

• Published in: Physica A Vol. 547; p. 124403
• Main Authors: Secrest, J.A., Conroy, J.M., Miller, H.G.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.06.2020
• Subjects: Continuous media; Maximum entropy principle; Continuous media; Maximum entropy principle
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2020.124403

Distribution functions of many static transport equations are found using the Maximum Entropy Principle. The equations of constraint which contain the relevant dynamical information are simply the low-lying moments of the distributions. Systems subject to conservative forces have also been considered. In this approach, determining the solutions to the transport equations no longer requires solving a partial differential equation but instead experimentally determining the low-lying moments and potentials. •Generalized solutions to the partial differential equations.•A new paradigm for considering general solutions to transport equations and their relationship to measured quantities.•And explicit applications of these solutions to equations that: have not been seen in the literature, have initial solutions, and have unusual potentials associated with external forces.