Effective conductivity and skew Brownian motion
- Cite this article as:
- Lang, R. J Stat Phys (1995) 80: 125. doi:10.1007/BF02178356
We consider heat conduction in a periodic body which is composed of finitely many different components. The effective conductivity is represented in terms of skew Brownian motion. The representation formula is a fluctuation-dissipation relation. The dissipation term in this formula is related to the transmission of heat through the surface separating the different components of the body; it is described by the skew reflections of Brownian motion at these surfaces. The problems caused by the discontinuity of the microscopic conductivity are handled in the framework of Dirichlet forms.