  Stochastic thermodynamics and the associated fluctuation relations provide
the means to extend the fundamental laws of thermodynamics to small scales and
systems out of equilibrium. The fluctuating thermodynamic variables are usually
treated in the context of either isolated Hamiltonian evolution, or Markovian
dynamics in open systems. However, there is no reason a priori why the
Markovian approximation should be valid in driven systems under non-equilibrium
conditions. In this work we introduce an explicitly non-Markovian model of
dynamics of an open system, where the correlations between the system and the
environment drive a subset of the environment out of equilibrium. Such a an
environment gives rise to a new type of non-Markovian entropy production term.
Such non-Markovian components must be taken into account in order to recover
the fluctuation relations for entropy. As a concrete example, we explicitly
derive such modified fluctuation relations for the case of an overheated single
electron box.
