  The irreversibility of trajectories in stochastic dynamical systems is linked
to the structure of their causal representation in terms of Bayesian networks.
We consider stochastic maps resulting from a time discretization with interval
\tau of signal-response models, and we find an integral fluctuation theorem
that sets the backward transfer entropy as a lower bound to the conditional
entropy production. We apply this to a linear signal-response model providing
analytical solutions, and to a nonlinear model of receptor-ligand systems. We
show that the observational time \tau has to be fine-tuned for an efficient
detection of the irreversibility in time-series.
