  We consider particle transport under the influence of time-varying driving
forces, where fluctuation relations connect the statistics of pairs of time
reversed evolutions of physical observables. In many "mesoscopic" transport
processes, the effective many-particle dynamics is dominantly classical, while
the microscopic rates governing particle motion are of quantum-mechanical
origin. We here employ the stochastic path integral approach as an optimal tool
to probe the fluctuation statistics in such applications. Describing the
classical limit of the Keldysh quantum nonequilibrium field theory, the
stochastic path integral encapsulates the quantum origin of microscopic
particle exchange rates. Dynamically, it is equivalent to a transport master
equation which is a formalism general enough to describe many applications of
practical interest. We apply the stochastic path integral to derive general
functional fluctuation relations for current flow induced by time-varying
forces. We show that the successive measurement processes implied by this setup
do not put the derivation of quantum fluctuation relations in jeopardy. While
in many cases the fluctuation relation for a full time-dependent current
profile may contain excessive information, we formulate a number of reduced
relations, and demonstrate their application to mesoscopic transport. Examples
include the distribution of transmitted charge, where we show that the
derivation of a fluctuation relation requires the combined monitoring of the
statistics of charge and work.
