The information-theoretic foundation of thermodynamic work extraction

In this paper I demonstrate a novel distinction between work and heat, in terms of the distinguishability of states. Specifically, I show that if it is possible to extract different amounts of work deterministically from a physical system prepared in any one of a set of states, then those states must be distinguishable from one another. This result is formulated independently of scale and of particular dynamical laws; it also provides a novel connection between thermodynamics and information theory, established via the law of conservation of energy. This connection, unlike the well-known one between information and the second law, is exact, i.e., it does not depend on coarse-graining or ensemble approximation. Albeit compatible with these conclusions, existing thermodynamics approaches cannot provide a result of such generality, because they are scale-dependent (relying on ensembles or coarse-graining) or tied to particular dynamical laws. This result provides a foundation for thermodynamics that is both broader and more secure than existing ones, with implications for the theory of von Neumann’s universal constructor.