  The wide-band limit is a commonly used approximation to analyze transport
through nanoscale devices. In this work we investigate its applicability to the
study of charge and heat transport through molecular break junctions exposed to
voltage biases and temperature gradients. We find that while this approximation
faithfully describes the long-time charge and heat transport, it fails to
characterize the short-time behavior of the junction. In particular, we find
that the charge current flowing through the device shows a discontinuity when a
temperature gradient is applied, while the energy flow is discontinuous when a
voltage bias is switched on and even diverges when the junction is exposed to
both a temperature gradient and a voltage bias. We provide an explanation for
this pathological behavior and propose two possible solutions to this problem.
