  The stochastic thermodynamics of systems with a few degrees of freedom has
been studied extensively so far. We would like to extend the study to systems
with more degrees of freedom and even further-continuous fields with infinite
degrees of freedom. The simplest case for a continuous stochastic field is the
Edwards-Wilkinson elastic manifold. It is an exactly solvable model of which
the heat statistics in the relaxation process can be calculated analytically.
The cumulants require a cutoff spacing to avoid ultra-violet divergence. The
scaling behavior of the heat cumulants with time and the system size as well as
the large deviation rate function of the heat statistics in the large size
limit is obtained.
