Generalized fluctuation-dissipation relations in confined geometries and concentrated conditions

his article extends the fluctuation-dissipation analysis to generic complex fluids in confined geometries and to all the cases the hydromechanic fluid-interaction kernels may depend on the particle position. This represents a completely new way of enforcing fluctuation-dissipation theory just because the primary target is to derive an explicit functional expression for the hydromechanic force (that is unavailable from linear hydrodynamic theory) from fundamental thermodynamic principles at equilibrium (while in the classical Kubo theory the memory kernels are explicitly known, stemming from the mean-field hydromechanics of fluid-particle interactions). In this way, either the representation of hydromechanic interactions and the explicit representation of the thermal forces are derived at the same time from thermodynamic principles. The physical and conceptual implications of these results are addressed. The theory can be extended to concentrated conditions and to suspensions, as well as to active particle in confined geometries accounting for the most general linear fluid-dynamic conditions.