Information Thermodynamics in Generalized Probabilistic Theories

TL;DR

This paper develops an information thermodynamics framework within Generalized Probabilistic Theories (GPTs), analyzing measurement costs and second law compliance, revealing conditions for thermodynamic consistency and potential violations.

Contribution

It introduces a unified, model-independent approach to thermodynamics in GPTs, linking measurement, entropy, and work extraction, and clarifies conditions for second law adherence.

Findings

No work extraction contradicts the second law if entropy nondecrease is maintained.

Sufficient conditions for thermodynamic consistency are derived for various entropy definitions.

Explicit GPT models demonstrate possible second law violations through specific measurement cycles.

Abstract

Generalized Probabilistic Theories (GPTs) provide a unified framework for describing probabilistic physical theories, encompassing classical and quantum theories as well as hypothetical theories beyond quantum mechanics. Since most GPTs are highly unrealistic and far removed from known physical theories, it is important to constrain them by physically reasonable principles. One of the most important such principles is consistency with thermodynamics, which has been extensively studied through toy models involving semipermeable membranes (SPMs) implementing measurements. On the other hand, information thermodynamics, which plays a central role in understanding the relationship between measurement and thermodynamics in classical and quantum theory, has remained largely undeveloped in GPTs. In this work, we construct information thermodynamics in GPTs and provide a unified framework for analyzing the relationship between measurement, feedback, information erasure, and the second law of thermodynamics. We also formulate a general framework for SPM models and analyze the thermodynamic cost of measurements implemented by SPMs. As a result, we show that no work can be extracted in contradiction with the second law as long as the measurement processes are consistent with entropy nondecrease, and derive sufficient conditions for this property for several entropy definitions proposed in GPTs. Moreover, by considering measurement processes violating these conditions, we construct explicit GPT systems realizing isothermal SPM cycles from which positive work can be extracted. These results demonstrate that violations of the second law can arise from the lack of fundamental entropy properties or discrepancies between entropy definitions, and provide a unified and model-independent foundation for understanding the relationship between thermodynamics and measurement in GPTs.