  We explore the effects of quantum mechanical squeezing on the nonequilibrium
fluctuations of bosonic transport between two squeezed harmonic reservoirs and
a two level system. A standard full counting statistics technique based on a
quantum master equation is employed. We derive a nonzero thermodynamic affinity
under equal temperature setting of the two squeezed reservoirs. The odd
cumulants are shown to be independent of squeezing under symmetric conditions,
whereas the even cumulants depend nonlinearly on the squeezing parameters. The
odd and even cumulants saturate at two different but unique values which are
identified analytically. Further, squeezing always increases the magnitude of
the even cumulants in comparison to the unsqueezed case. We also recover a
steady state fluctuation theorem with squeezing dependent thermodynamic
affinity and demonstrate the robustness of a steadystate thermodynamic
uncertainty relationship.
