# Microreversibility, fluctuations, and nonlinear transport in transistors

## TL;DR

This paper introduces a stochastic model for transistor charge transport that respects thermodynamic laws and microreversibility, verifying fundamental fluctuation relations and nonlinear transport properties through numerical analysis.

## Contribution

It develops a comprehensive stochastic framework for transistors that incorporates detailed balance, fluctuation theorems, and nonlinear transport, advancing theoretical understanding.

## Key findings

- Verification of the signal amplification under working conditions.
- Confirmation of the fluctuation theorem for joint electric currents.
- Numerical evidence of Onsager relations and their nonlinear extensions.

## Abstract

We present a stochastic approach for charge transport in transistors. In this approach, the electron and hole densities are governed by diffusion-reaction stochastic differential equations satisfying local detailed balance and the electric field is determined with the Poisson equation. The approach is consistent with the laws of electricity, thermodynamics, and microreversibility. In this way, the signal amplifying effect of transistors is verified under their working conditions. We also perform the full counting statistics of the two electric currents coupled together in transistors and we show that the fluctuation theorem holds for their joint probability distribution. Similar results are obtained including the displacement currents. In addition, the Onsager reciprocal relations and their generalizations to nonlinear transport properties deduced from the fluctuation theorem are numerically shown to be satisfied.