  We experimentally study negative fluctuations of stochastic entropy
production in an electronic double dot operating in nonequilibrium steady-state
conditions. We record millions of random electron tunneling events at different
bias points, thus collecting extensive statistics. We show that for all bias
voltages the experimental average values of the minima of stochastic entropy
production lie above $-k_B$, where $k_B$ is the Boltzmann constant, in
agreement with recent theoretical predictions for nonequilibrium steady states.
Furthermore, we also demonstrate that the experimental cumulative distribution
of the entropy production minima is bounded, at all times and for all bias
voltages, by a universal expression predicted by the theory. We also extend our
theory by deriving a general bound for the average value of the maximum heat
absorbed by a mesoscopic system from the environment and compare this result
with experimental data. Finally, we show by numerical simulations that these
results are not necessarily valid under non-stationary conditions.
