  In order to stabilize the behavior of noisy systems, confining it around a
desirable state, an effort is required to suppress the intrinsic noise. This
noise suppression task entails a cost. For the important case of thermal noise
in an overdamped system, we show that the minimum cost is achieved when the
system control parameters are held constant: any additional deterministic or
random modulation produces an increase of the cost. We discuss the implications
of this phenomenon for those overdamped systems whose control parameters are
intrinsically noisy, presenting a case study based on the example of a Brownian
particle optically trapped in an oscillating potential.
