Abstract
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.
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Lang, R. Effective conductivity and skew Brownian motion. J Stat Phys 80, 125–146 (1995). https://doi.org/10.1007/BF02178356
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DOI: https://doi.org/10.1007/BF02178356