Information transduction with multiple states

This thesis investigates information transduction in biological systems, focusing on the ability of an entity to extract information from a noisy environment using limited degrees of freedom, while minimizing the associated relative thermodynamic cost. Starting from a foundational three-component model, composed of a probe (y) that extracts information, a membrane (x) representing the accessible interface, and an active bath (η) acting as the information source, we generalize the system architecture to an arbitrary number of membrane states and active baths. To analyze the composition of the information driving the optimization of the sensory couplings, we employ Partial Information Decomposition (PID) on more complex architectures, considering systems with two membranes and one bath (M=2, N=1), and vice versa (M=1, N=2). By doing so, we are able to see whether synergy or redundancy in the accessible degrees of freedom is associated with a higher information transfer from the environment. We develop a framework that optimizes internal sensory parameters to maximize information extraction under a constraint of equal relative dissipation (the relative entropy production rate induced by the coupling parameters), ensuring a fair comparison with the baseline model. We find that the prevalence of synergistic or redundant information is closely associated with the system architecture. For the M=2, N=1 topology, synergistic information is generally favored, whereas for the M=1, N=2 case redundant information generally plays a more prominent role. Within both architectures, the optimal allocation of sensory resources is not uniform across parameter space: as the system transitions between different regimes, individual sensory couplings are observed to switch on or off, coinciding with structural transitions in the optimal configuration. These transitions are associated with the interplay between the environmental drive (σ) and the internal structural couplings (k) of the system.