Temperature and voltage probes far from equilibrium

We consider an open system of noninteracting electrons consisting of a small sample connected to several reservoirs and temperature or voltage probes. We study the nonlinear system of equations that determines the probe parameters. We show that it has a unique solution, which can be computed with a fast converging iterative algorithm. We illustrate our method with two well-known models: the three-terminal system and the open Aharonov-Bohm interferometer.