  The Langevin equation greatly simplifies the mathematical expression of the
effects of thermal noise by using only two terms, a dissipation term, and a
random-noise term. The Langevin description was originally applied to a system
in contact with a single heat reservoir; however, many recent studies have also
adopted a Langevin description for systems connected to multiple heat
reservoirs. This is accomplished through the introduction of a simple summation
for the dissipation and random-noise terms associated with each reservoir.
However, the validity of this simple addition has been the focus of only
limited discussion and has raised several criticisms. Moreover, this additive
description has never been either experimentally or numerically verified,
rendering its validity is still an open question. Here, we perform molecular
dynamics simulations for a Brownian system in simultaneous contact with
multiple heat reservoirs to check the validity of this additive approach. Our
simulation results confirm that the effect of multiple heat reservoirs is
additive in general.
  A very small deviation in the total amount of dissipation and associated
noise is found, but seems not significant within statistical errors. We find
that the steady-state properties satisfy the additivity perfectly and are not
affected by this deviation.
