Role of sufficient statistics in stochastic thermodynamics and its implication to sensory adaptation

A sufficient statistic is a significant concept in statistics, which means a probability variable that has sufficient information required for an inference task. We investigate the roles of sufficient statistics and related quantities in stochastic thermodynamics. Specifically, we prove that for general continuous-time bipartite networks, the existence of a sufficient statistic implies that an informational quantity called the sensory capacity takes the maximum. Since the maximal sensory capacity imposes a constraint that the energetic efficiency cannot exceed one-half, our result implies that the existence of a sufficient statistic is inevitably accompanied by energetic dissipation. We also show that, in a particular parameter region of linear Langevin systems, there exists the optimal noise intensity, at which the sensory capacity, the information-thermodynamic efficiency, and the total entropy production are optimized at the same time. We apply our general result to a model of sensory adaptation of E. Coli, and find that the sensory capacity is nearly maximal with experimentally realistic parameters, suggesting that E. Coli approximately realizes a sufficient statistic in signal transduction at the cost of energetic dissipation.