The Hot Bit I: The Szilard-Landauer Correspondence

We present a precise formulation of a correspondence between information and thermodynamics that was first observed by Szilard, and later studied by Landauer. The correspondence identifies available free energy with relative entropy, and provides a dictionary between information and thermodynamics. We precisely state and prove this correspondence. The paper should be broadly accessible since we assume no prior knowledge of information theory, developing it axiomatically, and we assume almost no thermodynamic background.