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We consider particle transport under the influence of time-varying drivingforces, where fluctuation relations connect the statistics of pairs of timereversed evolutions of physical observables. In many "mesoscopic" transportprocesses, the effective many-particle dynamics is dominantly classical, whilethe microscopic rates governing particle motion are of quantum-mechanicalorigin. We here employ the stochastic path integral approach as an optimal toolto probe the fluctuation statistics in such applications. Describing theclassical limit of the Keldysh quantum nonequilibrium field theory, thestochastic path integral encapsulates the quantum origin of microscopicparticle exchange rates. Dynamically, it is equivalent to a transport masterequation which is a formalism general enough to describe many applications ofpractical interest. We apply the stochastic path integral to derive generalfunctional fluctuation relations for current flow induced by time-varyingforces. We show that the successive measurement processes implied by this setupdo not put the derivation of quantum fluctuation relations in jeopardy. Whilein many cases the fluctuation relation for a full time-dependent currentprofile may contain excessive information, we formulate a number of reducedrelations, and demonstrate their application to mesoscopic transport. Examplesinclude the distribution of transmitted charge, where we show that thederivation of a fluctuation relation requires the combined monitoring of thestatistics of charge and work.

Transient fluctuation relations for time-dependent particle transport