Journal of Statistical Physics, Vol. 80, Nos. 1/2. 1995. p. 125-146.
We consider heat conduction in a periodic body which is composed of fmitely 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.