  We study nonequilibrium thermodynamics of complex information flows induced
by interactions between multiple fluctuating systems. Characterizing
nonequilibrium dynamics by causal networks (i.e., Bayesian networks), we obtain
novel generalizations of the second law of thermodynamics and the fluctuation
theorem, which include an informational quantity characterized by the topology
of the causal network. Our result implies that the entropy production in a
single system in the presence of multiple other systems is bounded by the
information flow between these systems. We demonstrate our general result by a
simple model of biochemical adaptation.
