  We discuss the stochastic thermodynamics of systems that are described by a
time-dependent density field, for example simple liquids and colloidal
suspensions. For a time-dependent change of external parameters, we show that
the Jarzynski relation connecting work with the change of free energy holds if
the time evolution of the density follows the Kawasaki-Dean equation.
Specifically, we study the work distributions for the compression and expansion
of a two-dimensional colloidal model suspension implementing a practical
coarse-graining scheme of the microscopic particle positions. We demonstrate
that even if coarse-grained dynamics and density functional do not match, the
fluctuation relations for the work still hold albeit for a different, apparent,
change of free energy.
