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.

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