  We derive a generalized version of the work fluctuation theorem for
nonequilibrium systems with spatio-temporal temperature fluctuations. For
chi-square distributed inverse temperature we obtain a generalized fluctuation
theorem based on q-exponentials, whereas for other temperature distributions
more complicated formulae arise. Since q-exponentials have a power law decay,
the decay rate in this generalized fluctuation theorem is much slower than the
conventional exponential decay. This implies that work fluctuations can be of
relevance for the design of micro and nano structures, since the work done on
the system is relatively much larger than in the conventional fluctuation
theorem.
