Fluctuations in inhomogeneous systems: From biopolymers through glasses to Casimir-like forces

Both thermal fluctuations and material inhomogeneity/disorder play a major role in many branches of science. This talk will focus on various aspects of the interplay between the two. First, we consider the spatial distribution of thermal fluctuational energy and derive universal bounds for internal-stress-free systems. In addition, we show that in 1D systems the thermal energy is equally partitioned even among coupled degrees of freedom. Applications to severing of actin filaments and protein unfolding are discussed. Then, we consider fluctuations in residually-stressed systems and their coupling to anharmonicity. In the context of glassy systems, we show that thermal energy van be spatially localized and suggest that it might serve as a useful structural diagnostic tool, e.g. for identifying glassy lengthscales and precursors to plastic events under driving forces. Lastly, we consider the continuum approach (Statistical Field Theory) to analyzing fluctuations in inhomogeneous systems, and demonstrate fundamental discrepancies between the continuum and the discrete theories in explicit calculations of some, but not all, fluctuation-induced (Casimir-like) forces.