  Nonequilibrium systems exchange the energy with an environment in the form of
work and heat. The work done on a system obeys the fluctuation theorem, while
the dissipated heat which differs from the work by the internal energy change
does not. We derive the modified fluctuation relation for the heat in the
overdamped Langevin system. It shows that mutual correlations among the work,
the heat, and the internal energy change are responsible for the different
fluctuation property of the work and the heat. The mutual correlation is
investigated in detail in a two-dimensional linear diffusion system. We develop
an analytic method which allows one to calculate the large deviation function
for the joint probability distributions. We find that the heat and the internal
energy change have a negative correlation, which explains the reason for the
breakdown of the fluctuation theorem for the heat.
