  The deep connection between thermodynamics, computation, and information is
now well established both theoretically and experimentally. Here, we extend
these ideas to show that thermodynamics also places fundamental constraints on
statistical estimation and learning. To do so, we investigate the constraints
placed by (nonequilibrium) thermodynamics on the ability of biochemical
signaling networks within cells to estimate the concentration of an external
signal. We show that accuracy is limited by energy consumption, suggesting that
there are fundamental thermodynamic constraints on statistical inference.
