  The total entropy production generated by the dynamics of an externally
driven systems exchanging energy and matter with multiple reservoirs and
described by a master equation is expressed as the sum of three contributions,
each corresponding to a distinct mechanism for bringing the system out of
equilibrium: nonequilibrium initial conditions, external driving, and breaking
of detailed balance. We derive three integral fluctuation theorems (FTs) for
these contributions and show that they lead to the following universal
inequality: an arbitrary nonequilibrium transformation always produces a change
in the total entropy production greater or equal than the one produced if the
transformation is done very slowly (adiabatically). Previously derived
fluctuation theorems can be recovered as special cases. We show how these FTs
can be experimentally tested by performing the counting statistics of the
electrons crossing a single level quantum dot coupled to two reservoirs with
externally varying chemical potentials. The entropy probability distributions
are simulated for driving protocols ranging from the adiabatic to the sudden
switching limit.
