  Small systems in contact with a heat bath evolve by stochastic dynamics. Here
we show that, when one such small system is weakly coupled to another one, it
is possible to infer the presence of such weak coupling by observing the
violation of the steady state fluctuation theorem for the partial entropy
production of the observed system. We give a general mechanism due to which the
violation of the fluctuation theorem can be significant, even for weak
coupling. We analytically demonstrate on a realistic model system that this
mechanism can be realized by applying an external random force to the system.
In other words, we find a new fluctuation theorem for the entropy production of
a partial system, in the limit of weak coupling.
