Emergence and Breaking of Duality Symmetry in Generalized Fundamental Thermodynamic Relations

Abstract

Thermodynamics as limiting behaviors of statistics is generalized to arbitrary systems with probability a priori where the thermodynamic infinite-size limit is replaced by a multiple-measurement limit. A duality symmetry between Massieu’s and Gibbs’s entropy arises in the limit of infinitely repeated observations, yielding the Gibbs equation and Hill-Gibbs-Duhem equation (HGDE) as a dual pair. If a system has a 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.



Citation
Emergence and Breaking of Duality Symmetry in Generalized Fundamental Thermodynamic Relations Physical Review Letters (IF9.185), Pub Date : 2022-04-15, DOI: 10.1103/physrevlett.128.150603 Zhiyue Lu, Hong Qian