Optimal finite-time statistical inference

Statistical inference is an inherently dissipative process, as encoding new beliefs in a physical memory requires work. Previous studies have characterized the minimal thermodynamic costs associated with parametric control of physical systems, but the corresponding problem for belief updating remains largely unexplored. Here, we develop a minimal nonequilibrium model to study the general question of the thermodynamic costs of statistical inference and to investigate optimal protocols that minimize energetic dissipation during inference. Our results provide a framework for constructing the thermodynamic analogue of Bayesian updating, in which belief dynamics achieve thermodynamic rather than statistical optimality.