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We study the thermal Casimir effect between two thick slabs composed of plane-parallel layers of random dielectric materials interacting across an intervening homogeneous dielectric. It is found that the effective interaction at long distances is self averaging and is given by a description in terms of effective dielectric functions. The behavior at short distances becomes random (sample dependent) and is dominated by the local values of the dielectric function proximal to each other across the dielectrically homogeneous slab.
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We study the thermal fluctuation induced interactions between two surfaces containing Brownian charges which are held at different temperatures. Using a dynamical form of Debye-Huckel theory implemented within the stochastic equation for the density of mobile Brownian charges, we derive expressions for the average force between the two surfaces as well as its variance. The latter is found both for the normal, of finite mean, as well as the lateral force, of zero mean, between the surfaces.
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