Emergence and Breaking of Duality Symmetry in Generalized Fundamental Thermodynamic Relations

Zhiyue Lu and Hong Qian
Phys. Rev. Lett. 128, 150603 – Published 15 April 2022

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.

  • Received 13 November 2021
  • Revised 22 January 2022
  • Accepted 11 March 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.150603

© 2022 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Zhiyue Lu*

  • Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290, USA

Hong Qian

  • Department of Applied Mathematics, University of Washington, Seattle, Washington 98195-3925, USA

  • *zhiyuelu@unc.edu
  • hqian@u.washington.edu

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Vol. 128, Iss. 15 — 15 April 2022

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