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

TL;DR

This paper reconstructs thermodynamics from an information-theoretic perspective using axioms based on observed system aspects and reference measures, leading to a unified framework for equilibrium and nonequilibrium processes.

Contribution

It introduces an axiomatic approach to thermodynamics grounded in information volume and path-space KL divergence, unifying equilibrium and nonequilibrium thermodynamics.

Findings

Derives thermodynamic variables as conjugates of an information volume functional.

Defines heat and entropy production without relying on local detailed balance.

Provides a unified interpretation of dissipation and information flow in stochastic dynamics.

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.