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Thermodynamics with and without irreversibility

Wallace, David (2023) Thermodynamics with and without irreversibility. [Preprint]


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Working inside 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. Phenomenological thermodynamics is reconstructed via the `equilibration' coarse-graining where a system is coarse-grained to a canonical distribution; finer-grained forms of thermodynamics differ from phenomenological thermodynamics only in that some states of a system possess a free energy that can be extracted by reversibly transforming the system (as close as possible) to a canonical distribution. Exceeding the limits of phenomenological thermodynamics thus requires both finer-grained control of a system and finer-grained information about its state. 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, even the entirely reversible limit where no coarse-graining is appealed to at all. I illustrate these points via a discussion of Maxwell's demon.

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Item Type: Preprint
Additional Information: 41 pages
Keywords: thermodynamics statistical mechanics control theory resource theory entropy Maxwell's demon
Subjects: Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Depositing User: Professor David Wallace
Date Deposited: 02 Jul 2023 13:12
Last Modified: 02 Jul 2023 13:12
Item ID: 22273
Subjects: Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Date: June 2023

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