Fractional Generalization of Fick's Law: A Microscopic Approach

I. Calvo, R. Sánchez, B. A. Carreras, B. Ph. van Milligen
2007 Physical Review Letters  
In the study of transport in inhomogeneous systems it is common to construct transport equations invoking the inhomogeneous Fick law. The validity of this approach requires that at least two ingredients be present in the system. First, finite characteristic length and time scales associated to the dominant transport process must exist. Secondly, the transport mechanism must satisfy a microscopic symmetry: global reversibility. Global reversibility is often satisfied in nature. However, many
more » ... . However, many complex systems exhibit a lack of finite characteristic scales. In this Letter we show how to construct a generalization of the inhomogeneous Fick law that does not require the existence of characteristic scales while still satisfying global reversibility.
doi:10.1103/physrevlett.99.230603 pmid:18233351 fatcat:gmaqwz3vt5h7rjsmtdmr53o7s4