Thermodynamics Reconstructed from Information Theory:An Axiomatic Framework via Information-Volume Constraints and Path-Space KL Divergence

Abstract: We develop an axiomatic reconstruction of thermodynamics based entirely on two primitive components: a description of what aspects of a system are observed and a reference measure that encodes the underlying descriptive convention. These ingredients define an "information volume" for each observational cell. By incorporating the logarithm of this volume as an additional constraint in a minimum-relative-entropy inference scheme, temperature, chemical potential, and pressure arise as conjugate variables of a single information-theoretic functional. This leads to a Legendre-type structure and a first-law-like relation in which pressure corresponds to information volume rather than geometric volume. For nonequilibrium dynamics, entropy production is characterized through the relative-entropy asymmetry between forward and time-reversed stochastic evolutions. A decomposition using observational entropy then separates total dissipation into system and environment contributions. Heat is defined as the part of dissipation not accounted for by the system-entropy change, yielding a representation that does not rely on local detailed balance or a specific bath model. We further show that the difference between joint and partially observed dissipation equals the average of conditional relative entropies, providing a unified interpretation of hidden dissipation and information-flow terms as projection-induced gaps.