Superstatistical generalization of the work fluctuation theorem

We derive a generalized version of the work fluctuation theorem for non-equilibrium systems with spatio-temporal temperature fluctuations. For χ2-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- or nano-structures, since the work done on the system is relatively much larger than in the conventional fluctuation theorem.