14 - Bulk dynamics and response

Summary

Introduction

Up to now, we have considered only those inherent microscopic dynamics in a material that are present at equilibrium and are driven by the thermal energy content of the material itself. Here, in our last chapter dealing with dynamics, we consider instead the macroscopic, bulk dynamics of materials in non-equilibrium situations where an external force is applied or removed. Examples include the stretching or bending of a solid that results from application of a mechanical force, or the polarization of a dielectric material resulting when an external electric field is applied.

Several common features emerge in the response of a material to an external force or field. In all cases, there is some aspect of elasticity by which application of the force results in the storage of potential energy, that is returned when the force is removed. In all cases, this storage of energy is accompanied by some element of viscous drag or damping by which a portion of the work done during the deformation is lost in the form of heat. Like friction, this damping is a microscopic feature inherent in the thermodynamic fluctuations, and the energy lost during the deformation is returned to the same thermal bath from which it was derived. In fact, we will show that an important theorem exists, known as the fluctuation–dissipation theorem, which relates the macroscopic dissipation of energy in these bulk, non-equilibrium, processes directly to the inherent microscopic fluctuations present at equilibrium.