On the applicability of entropy potentials in transport problems
1 Program in Physical Biology, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, MD 20892, USA
2 Mathematical and Statistical Computing Laboratory, Division of Computational Bioscience, Center for Information Technology, National Institutes of Health, Bethesda, MD 20892, USA
Received: 17 October 2014
Revised: 5 November 2014
Published online: 15 December 2014
Transport in confined structures of varying geometry has become the subject of growing attention in recent years since such structures are ubiquitous in biology and technology. In analyzing transport in systems of this type, the notion of entropy potentials is widely used. Entropy potentials naturally arise in one-dimensional description of equilibrium distributions in multidimensional confined structures. However, their application to transport problems requires some caution. In this article we discuss such applications and summarize the results of recent studies exploring the limits of applicability. We also consider an example of a transport problem in a system of varying geometry, where the conventional approach is inapplicable since the geometry changes abruptly. In addition, we demonstrate how the entropy potential can be used to analyze optimal transport through a three-dimensional cosine-shaped channel.
© EDP Sciences, Springer-Verlag, 2014