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The irreversibility of trajectories in stochastic dynamical systems is linkedto 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 theoremthat sets the backward transfer entropy as a lower bound to the conditionalentropy production. We apply this to a linear signal-response model providinganalytical solutions, and to a nonlinear model of receptor-ligand systems. Weshow that the observational time \tau has to be fine-tuned for an efficientdetection of the irreversibility in time-series.

A fluctuation theorem for time-series of signal-response models with the backward transfer entropy