  Multivariate fluctuation relations are established in three stochastic models
of transistors, which are electronic devices with three ports and thus two
coupled currents. In the first model, the transistor has no internal state
variable and particle exchanges between the ports is described as a Markov jump
process with constant rates. In the second model, the rates linearly depend on
an internal random variable, representing the occupancy of the transistor by
charge carriers. The third model has rates nonlinearly depending on the
internal occupancy. For the first and second models, finite-time multivariate
fluctuation relations are also established giving insight into the convergence
towards the asymptotic form of multivariate fluctuation relations in the
long-time limit. For all the three models, the transport properties are shown
to satisfy Onsager's reciprocal relations in the linear regime close to
equilibrium as well as their generalizations holding in the nonlinear regimes
farther away from equilibrium, as a consequence of microreversibility.
