Uploaded February 2025 | Updated September 2026, 2 hours ago

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Thermodynamics with and without irreversibility

Working within the control-theoretic framework for understanding thermodynamics, I develop a systematic way to characterize thermodynamic theories via their compatibility with various notions of coarse-graining, which can be thought of as parametrizing an agent’s degree of control of a system’s degrees of freedom, and explore the features of those theories. I consider the status of the Second Law in this framework, and distinguish two versions: the principle that entropy does not decrease, and the Kelvin/Clausius statements about the impossibility of transforming heat to work, or moving heat from a cold body to a hotter body, in a cyclic process. The former should be understood as relative to a coarse-graining, and can be violated given finer control than that coarse-graining permits; the latter is absolute, and binds any thermodynamic theory compatible with the laws of physics. I illustrate these points via a discussion of Maxwell’s demon.