  In nature stationary nonequilibrium systems cannot exist on their own, rather
they need to be driven from outside in order to keep them away from
equilibrium. While the internal mean entropy of such stationary systems is
constant, the external drive will on average increase the entropy in the
environment. This external entropy production is usually quantified by a simple
formula, stating that each microscopic transition of the system between two
configurations $c \to c'$ with rate $w_{c\to c'}$ changes the entropy in the
environment by $\Delta S_{\rm env} = {\ln w_{c \to c'}}-{\ln w_{c' \to c}}$.
According to this formula irreversible transitions $c \to c'$ with a vanishing
backward rate $w_{c'\to c}=0$ would produce an infinite amount of entropy.
However, in experiments designed to mimic such processes, a divergent entropy
production, that would cause an infinite increase of heat in the environment,
is not seen. The reason is that in an experimental realization the backward
process can be suppressed but its rate always remains slightly positive,
resulting in a finite entropy production. The paper discusses how this entropy
production can be estimated and specifies a lower bound depending on the
observation time.
