5Dynamics

III Theoretical Physics of Soft Condensed Matter

5 Dynamics

We now want to understand dynamics, namely if we have a system out of

equilibrium, how will it evolve in time? Physically, such situations are usually

achieved by rapidly modifying external parameters of a system. For example,

if the system is temperature-dependent, one may prepare a sample at high

temperature so that the system is in a homogeneous state, and then quench the

system by submerging it in water to lower the temperature rapidly. The system

will then slowly evolve towards equilibrium.

Before we think about the problem of dynamics, let’s think about a more

fundamental question — what is it that is preventing the system from collapsing

to the ground state entirely, as opposed to staying in the Boltzmann distribution?

The answer is that our system is in contact with a heat bath, which we can

model as some random noise driving the movement of our particles. This gives a

dynamical way of achieving the Boltzmann distribution. When the system is

out of equilibrium, the random noise is still present and drives our system. The

key point is that the properties of the noise can be derived from the fact that at

equilibrium, they give the Boltzmann distribution.