Compositional Thermostatics

• Published in: arXiv.org
• Main Authors: Baez, John C, Lynch, Owen, Moeller, Joe
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 10.02.2023
• Subjects: Entropy; Mathematics - Category Theory; Mathematics - Mathematical Physics; Physics - Mathematical Physics; Quantum statistics; Statistical analysis; Statistical mechanics
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2111.10315

We define a thermostatic system to be a convex space of states together with a concave function sending each state to its entropy, which is an extended real number. This definition applies to classical thermodynamics, classical statistical mechanics, quantum statistical mechanics, and also generalized probabilistic theories of the sort studied in quantum foundations. It also allows us to treat a heat bath as a thermostatic system on an equal footing with any other. We construct an operad whose operations are convex relations from a product of convex spaces to a single convex space, and prove that thermostatic systems are algebras of this operad. This gives a general, rigorous formalism for combining thermostatic systems, which captures the fact that such systems maximize entropy subject to whatever constraints are imposed upon them.