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arXiv · 2009.12644

Emergence and Breaking of Duality Symmetry in Generalized Fundamental Thermodynamic Relations

Zhiyue Lu·Hong Qian
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Abstract

Thermodynamics as limiting behaviors of statistics is generalized to arbitrary system with probability {\it a priori} where thermodynamic infinite-size limit is replaced by multiple-measurement limit. A duality symmetry between Massieu's and Gibbs' entropy arises in the limit of infinitely repeated observations, yielding the Gibbs equation and Hill-Gibbs-Duhem equation (HGDE) as dual pair. If a system has thermodynamic limit satisfying Callen's postulate, entropy being an Eulerian function, the symmetry is lost: the HGDE reduces to the Gibbs-Duhem equation. This theory provides a de-mechanized foundation for classical and nanothermodynamics and offers a framework for distilling emergence from large data, free from underlying details.

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BibTeXRIS

Zhiyue Lu, Hong Qian. 2020-09-26. Emergence and Breaking of Duality Symmetry in Generalized Fundamental Thermodynamic Relations. https://doi.org/10.1103/physrevlett.128.150603

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