13 Classical time-dependent statistical mechanics
13.1 Ensembles of driven systems
Our discussion of both classical and quantum statistical mechanicshas thus far been
restricted to equilibrium ensembles. The most fundamental of these, the microcanonical
ensemble, consists of a collection of systems and evolving accordingto Hamilton’s
equations of motion in isolation from the surroundings. Other ensembles are generated
by coupling a physical system to a heat bath, a barostat, or a particle reservoir in order
to control other equilibrium thermodynamic variables. The equilibriumensembles
allow a wide variety of thermodynamic and structural properties ofsystems to be
computed.
However, there are many properties of interest that can only be measured by sub-
jecting the system to an external perturbation of some kind. Forexample, if we wish
to measure the coefficient of shear viscosity of a system, we could subject it to an
external shear force by placing the system between two movable plates, pulling the
plates in opposite directions (see Fig. 13.1), and measuring the response of the sys-
tem to the force caused by the plate motion. Properties of this type are known as
Fig. 13.1A model shearing experiment: A fluid placed between two plates is subject to a
shearing force by pulling the plates in opposite directions.