From Brownian Motion to Bending Beams

This chapter argues that the hydrodynamic, correlation function methodology discussed in “fluid” contexts is really the same methodology employed in materials science to determine effective values for quantities like conductivity, elasticity, stiffness. Thus, Einstein’s arguments discussed in the previous chapter have a bearing on what prima facie appear to be completely different problems. The mesoscale approach using representative volume elements and correlation functions to describe the important features of those representative volume elements is presented in some detail.

The Right Variables and Natural Kinds

This chapter argues that mesoscale parameters (order parameters and material parameters) are the natural variables by which we can characterize and understand lawful behaviors of many-body systems. It engages in a debate about whether the determination of natural kinds flows from metaphysical considerations about fundamentality and carving nature at its joins or from goal oriented aims of ones scientific methodology. The chapter argues for a scientific determination of the natural variables (at least in the case of many-body systems) based on the previous discussions of the hydrodynamic, correlation function approach. The Fluctuation-Dissipation theorem provides a justification for taking the mesoscale variables and parameters to be natural kinds.