Counting statistics and microreversibility in stochastic models of transistors

Abstract

Abstract Multivariate fluctuation relations are established in several stochastic models of transistors, which are electronic devices with three ports and thus two coupled currents. For all these 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. In the first model, which is related to the Ebers–Moll transport model for bipolar junction transistors, there is no internal state variable and particle exchanges between the ports are 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, as in single-electron transistors. 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.